Ke-Min Zhang's Publications (2005-)

The List of Publications (by field)

	01.	On Irregularity of Vertices for a Class of Tournaments, Nanjing Shiyuan Xuebao 1 (1980) 1--10. (with Wu Zheng Sheng and Zou Yuan)
	02.	A Necessary and Sufficient Condition for Arc-pancyclicity of Tournaments, Scientia Sinica (Chinese Edition)8 (1981) 915--919 and (English Edition)A25(3)(1982) 249--254. (with Wu Zheng Sheng and Zou Yuan) MR#83m:05070
	03.	On the Existence of a Class of Tournaments with Completely Strong Path-connectivity, Nanjing Daxue Xuebao 3 (1981) 303--307. (with Wu Zheng Sheng and Zou Yuan) MR#83j:05036
	04.	k-arc-cyclicity of T_s Graph, Nanjing Shiyuan Xuebao 1 (1981) 1--3. (with Wu Zheng Sheng and Zou Yuan)
	05.	Completely Strong Path-connected Tournaments,J. Combin Theory B 33(2) (1982) 166--177. MR#84e:05057
	06.	A Necessary and Sufficient Condition for Strong Connected k-partite Tournaments, Nanjing Shiyuan Xuebao 3 (1982)39--42. (with Wu Zheng Sheng)
	07.	A Kind of Counterexamples on Arc-pancyclic Tournaments, Acta Mathematicae Applicatae Sinica 6(1) (1983) 47--49. (with Wu Zheng Sheng and Zou Yuan) MR#85f:05068
	08.	A Necessary and Sufficient Condition for Completely Strong Path-connectivity of Tournaments,Chinese Ann. Math. A4 (1983) 385--392. (with Wu Zheng Sheng)MR#84m:05033
	09.	Vertex Even-pancyclicity in Bipartite Tournaments, J. of Nanjing University, Mathematical Biquarterly 1(1) (1984) 85--88. MR#86e:05049
	10.	Longest Paths and Cycles in Bipartite Oriented Graphs, J. of Graph Theory 11(3) (1987) 339--348. MR#88i:05119
	11.	On Lewin and Vitek's Conjecture about Exponent Set of Primitive Matrices, Linear Algebra and its Applications 96 (1987) 101--108. MR#88j:15019
	12.	On the Set of the Index of Maximum Density of Tournaments, J. of Nanjing University, Mathematical Biquarterly 4(2) (1987) 117--122. (with Wang Hong De and Hong Ji Zhi) MR#89g:05077
	13.	On the Power Sequence of Boolean Matrices---A Survey, The Second International Conference on Combinatorial Mathematics and Computing, Canberra,Australia (1987).
	14.	A Note of Upper Bound about the Index of Maximum Density of Nonnegative Matrices, Xinjiang Daxue Xuebao 5(1) (1988) 44--46. MR#90f:15025
	15.	Complementary Cycles Containing a Pair of Fixed Vertices in Bipartite Tournaments, Applied Mathematics--A Journal of Chinese Universities 3(3) (1988) 401--407. (with Song Zeng Min)
	16.	The Problems and Solutions in Graph Theory with Applications, QingHua University Press (1988). (with Lin Guo Ning and Zhang Zhong Fu)
	17.	The Exponent Set of Symmetric Primitive (0,1)-matrices with Zero Trace, Linear Algebra and its Applications 133 (1990) 121--131. (with Bolian Liu, McKay B.D. and Wormald N.C.) MR#91h:15018
	18.	On Vertex-pancyclic Graphs with the Distance Two Condition, J. of Nanjing University, Mathematical Biquarterly 7(2) (1990) 157--162. (with Song Zeng Min) MR#91m:05123
	19.	On Hamiltonian Bipartite Tournaments, ibid. 8(1) (1991) 6--10. (with Song Zeng Min and Wang Jian Zhong) MR#92k:05088
	20.	A Property of Total Colouring of Graphs, ibid. 8(2) (1991) 99--102. (with Zhang Zhong Fu and Li Xiao Dong)MR#92j:05082
	21.	A New Assignment Model and Its Algorithm, Ars Combinatoria 31 (1991) 217--221. (with Song Zeng Min) MR#92m:05153
	22.	Cycles in Digraphs---A Survey, J. of NanjingUniversity, (Special Issue about Graph Theory) 27 (1991) 188--215. (with Song Zeng Min) MR#93g:05064
	23.	The Value of the Ramsey Number R(3,8), J. Graph Theory 16(1) (1992) 99--105. (with McKay B.D.) MR#92m:05138
	24.	A Note on the Size Ramsey Number for Stars, J. Combinatorial Mathematics and Combinatorial Computing 11 (1992) 209--212. MR#93a:05096
	25.	The Exponent Set of Undirected Graph with the Minimum Odd Cycle Length r, J. of Nanjing University, Mathematical Biquarterly 9(1) (1992) 29--36. (with Miao Zheng Ke) MR#94a:05120
	26.	A Sufficient Condition for a Graph to Be Hamiltonian, ibid.9(2)(1992) 163--167. (with Song Zeng Min) MR#94a:05140
	27.	An Application of Assignment Model in Public Transits, Proceedings of ORSC'92 (1992) 711--712. (with Sun Zhi Yong)
	28.	Complementary Cycles Containing a Fixed Arc and a Fixed Vertex in Bipartite Tournaments, Ars Combinatoria 35 (1993) 265--269. (with Wang Jian Zhong) MR#93m:05113
	29.	On Edge-pancyclic Graphs, Soochow J. of Mathematics 19(1) (1993) 37--41. (with D.A, Holton) MR#93j:05097
	30.	On Generalized Vertex-pancyclic Graphs, Chinese J. of Mathematics 21(1) (1993) 91--98. (with D.A. Holton and Sheng Bau) MR#94a:05123
	31.	On Hamiltonian Bipartite Tournaments, J. of Mathematics 13(3) (1993) 351--356. (with Li Gui Rong, Wang Jian Zhong and Song Zeng Min) MR#96b:05067
	32.	A Note of Grunbaum Conjecture, J. of Gezhouba Institute of Hydro-electric Engineering 2 (1993) 90--92. (with Li Guang Chun)
	33.	On Two Conjectures of Connectivity about Locally Semicomplete Digraphs, J. of NanjingUniversity, Mathematical Biquarterly 10(2) (1993) 146--152. (with Bu Yue Hua) MR#96a:05094
	34.	The Uniqueness of (4,5)-cage, ibid. 11(1) (1994) 70--72. (with Li Guang Chun and Yao Tian Xing) MR#95i:05098
	35.	The Characterization of Symmetric Primitive Matrices with the Second Maximum Exponent, ibid. 11(2) (1994) 193--197. (with Wang Jian Zhong, Wei Fu Yi and Pan Jin Xiao) MR#:1340595
	36.	A Degree Characterisation of Pancyclicity, Discrete Mathematics 127 (1994) 23--29. (with R.E.L. Aldred and D.A. Holton) MR#95c:05071
	37.	Neighbourhood Unions and Hamiltonian Properties, Discrete Mathematics 133 (1994) 319--324. (with Song Zeng Min) MR#95h:05104
	38.	Complementary Cycles Containing a Fixed Arc in the Bipartite Tournaments, Discrete Mathematics 133 (1994) 325--328. (with Y. Manoussakis and Song Zeng Min) MR#95h:05083
	39.	The Exponent Set of Primitive (0,1)-matrices with Zero Trace, Xuzhou Shiyuan Xuebao 12(2) (1994) 4--7. (with Miao Zheng Ke)
	40.	On Antidirected Cycles and Paths in Bipartite Tournaments, Applied Mathematics---A J. of Chinese Universities A10(2) (1995) 203--208. (with Wang Jian Zhong and Li Gui Rong) MR#96d:05054
	41.	The Characterization of Symmetric Primitive Matrices with Exponent 2n-2r ( ≥n), Linear and Mulitilinear Algebra 39 (1995) 391--396. (with Cai Jun Liang) MR#97b:05097
	42.	Some Tree-stars Ramsey Numbers, Proceedings of the Second Asian Mathematical Conference 95 (1995) 287--291. (with Zhang Shu Sheng) MR#99g:05135
	43.	A New Idea for Hamiltonian Problem, Ars Combinatoria 43 (1996) 97--105. (with Song Zhen Min) MR#97e:05137
	44.	A Note on 4-regular 4-chromatic Graphs with Grith 4, Graph Theory Notes of New York XXX (1996) 35--36. (with Song Wen Jie, Wang Jian Zhong and Yao Tian Xing) MR#99h:05044
	45.	A New Sufficient Condition for D-circuits, J. of Nanjing University, Mathematical Biquarterly 13(1) (1996) 38--43. (with Ye Miaolin) MR#97f:05108
	46.	Some Localizations of Conditions for Long Cycle in Graphs, ibid.14(1) (1997) 10--14. (with Ye Miaolin) MR#98h:05122
	47.	A Sufficient Condition for 2-connected Hamilton Graphs, ibid. 14(2) (1997) 171-179. (with Pan Lin Qiang) MR#99c:05127
	48.	The Upper Bounds of the Generalized Maximum Density Index of Irreducible Boolean Matrices, Linear Algebra and Its Applications 256 (1997) 75--93. (with Chen Xi) MR#98g:15030
	49.	On the Exponent Set of Primitive Locally Semicomplete Digraphs, Applied Mathematics---A J. of Chinese Universities B12(3) (1997) 267--286 and J. of Nanjing University (Natural Science Edition) 31(3) (1995) 506--507. (with Bu Yue Hua) MR#99a:05060
	50.	The Total Chromatic Number of Psedo-outerplane Graphs, Applied Mathamatics--A J. of Chinese Universities B12(4) (1997)455--462. (with Wang Weifan) MR#98m:05074
	51.	On the Arc-pancyclicity of Local Tournaments, Ars Combinatoria 47 (1997)242--254. (with Bu Yue Hua) MR#98h:05116
	52.	A Proof of Melinkov's Conjecture for Case Δ=4, Chinese Science Bulletin (Chinese Edition) 3 (1998) 330--331 and (English Edition) 43(4) (1998) 352. (with Wang Weifan)
	53.	Some Local Conditions for Hamilton-connected Graphs, Soochow J. of Mathematics 24(3) (1998) 177--182. (with Pan Lin Qiang) MR#99f:05074
	54.	New Upper Bounds for Ramsey Numbers, European J. of Combinatorics 19 (1998) 391--394. (with Huang Yi Ru) MR#99b:05100
	55.	A New Upper Bound Formula for Two Color Classical Ramsey Numbers, J. of Combinatorial Mathematics and Combinatorial Computing 28 (1998) 347--350. (with Huang Yi Ru) MR#99j:05143
	56.	A Neighbourhood Union Condition for Vertex-pancyclicity, Applied Mathematics--A J. of Chinese Universities A13(1) (1998) 79--86. (with Ye Miaolin) MR#99g:05117
	57.	Two Order Exponent Set of Strong Connected Digraphs, J. of NanjingUniversity, Mathematical Biquarterly 15(1) (1998) 9--14. (with Miao Zheng Ke) MR#99f:05076
	58.	A Note on Cycles in Regular Multipartite Tournaments, ibid. 15(1) (1998) 73--75. (with Zhou Guofei and Yao Tian Xing) MR#99f:05050
	59.	On the Unique Coupled Coloring of Plane Graphs, ibid. 15(2)(1998) 163--167. (with Wang Weifan) MR#00c:05071
	60.	On the Critical Domination Number, Mathematica Applicata 11(3) (1998) 95--97. (with Ye Miaolin) MR#99m:05081
	61.	Edge-face Chormatic Number of Plane Graphs with High Maximum Degrees, Australasian J. of Combinatorics 18(1998) 235--244. (with Wang Weifan ) MR#99j:05076
	62.	A Sufficient Condition for a Semicomplete Multipartite Digraph to Be Hamiltonian, ibid. 19 (1999) 231--234. (with Zhou Guofei) MR#00b:05092
	63.	The List Chromatic Numbers of Some Planar Graphs, Applied Mathematics---A J. of Chinese Universities B14(1) (1999) 108--116. (with Lu Enyue) MR#00a:05084
	64.	Completely Strong Path-connectivity of Local Tournaments, Ars Combinatoria 51(1999) 249--268. (with Bu Yue Hua) MR#00a:05131
	65.	Δ-Matching and Edge-face Chromatic Numbers, Acta Mathematicae Applicatae Sinica 22(2) (1999)236--242. (with Wang Weifan) MR#00h:05179
	66.	γ-paths of Arcs in Regular Multipartite Tournaments, Bulletin of the Korean Mathemathical Society 36(2)(1999) 389--394. (with Yao Tian Xing and Guo Yubao) MR#00i:05086
	67.	The Local Exponent Sets of Primitive Digraphs Without Loop, J. of Nanjing University, Mathematical Biquarterly 16(1) (1999) 13--17. (with Miao Zhengke) MR#00e:05081
	68.	A Note on Arc Pancyclicity of Regular Ordinary Multipartite Tournaments ibid. 16(1) (1999) 62--64. (with Pan Linqiang and Zhou Guofei) MR#00e:05100
	69.	Hamiltonian Multipartite Tournaments, OR Transactions 3(3) (1999) 22--24. (with Zhou Guo Fei)
	70.	A Note on Hypertournaments, Chinese Science Bulletin (English Edition) 44(16) (1999) 1460--1462. (with Pan Linqiang and Zhou Guofei) MR#00h:05100
	71.	The Value of the Ramsey Number R(Cn,K4) Is 3(n-1)+1 (n≥4), The Australasian J. of Combinatorics 20(1999) 205--206. (with Yang Jian Sheng and Huang Yi Ru)MR1723874
	72.	Edge-face Coloring of 1-outerplane Graphs, Mathematica Applicata 12(4) (1999) 78--81. ( with Wang Weifan) MR#01b:05097
	73.	Pancyclic Out-arcs of a Vertex in Tournaments, Discrete Applied Mathematics 99(2000) 245--249. (with Yao Tian Xing and Guo Yubao) MR#00m:05112
	74.	A New Property of Binary Undirected de Bruijn Graphs, Chinese Annals of Mathematics B21(1) (2000) 39--42. (Xu Junming and Lu Changhong)MR#01c:05087
	75.	A Sufficient Condition for Oriented Graphs to Be Hamiltonian, Ars Combinatoria 55 (2000) 283--287. (with Pan Lin Qiang) MR#00m:05149
	76.	Equitable Coloring of Line Graphs and Complete γ-partite Graphs, Systems Science and Mathematics Science 13(2) (2000) 190--194. (with Wang Weifan) MR#01g:05055
	77.	Colorings of Hypergraphs, Advance in Mathematics 29(2) (2000) 115--136. (with Wang Weifan) MR#01f:05069
	78.	The Second Exponent Set of Primitive Digraphs, Chinese Annals of Mathematics B21(2) (2000) 233--236. (with Miao Zhengke) MR#01b:05106
	79.	The Local Exponents of Primitive Digraphs,Linear Algebra and Its Applications 307 (2000) 15--33 and 320 (2000)209--216. (with Miao Zhengke) MR#01c:05064, MR#01k:05090
	80.	New Results of B(27) And B(52), J. of NanjingUniversity, Mathematical Biquarterly, 17(1) (2000) 9--14. (with Zhou Jainguo) MR#:1771151
	81.	On Critical Ramsey Decompositions, ibid,17(1) (2000) 64--67. (with Shi Ling Sheng) MR#01b:05153
	82.	A Local Intersection Condition for n-extendable Graphs, ibid 17(2) (2000) 157--161. (with Pan Lin Qiang and Chen Xu Jin) MR#01m:05213
	83.	On a Conjecture Involving Cycle-complete Graph Ramsey Numbers, Australasian Journal of Combinatorics 22 (2000) 63--71. (with Bela Bollobas,Chula Jayawardene, Jiansheng Yang ,Huang Yi Ru,Cecil Rousseau) MR#01h:05069
	84.	Localization Theorem on Hamiltonian Graphs, Acta Mathematica Scientia 20(1) (2000) 76--78. (with Pan Lin Qiang and Zhou Guofei) MR#01b:05136
	85.	On Score Sequence of k-hypertournaments, European J. of Combinatorics 21(8) (2000) 993--1000. (with Zhou Guofei and Yao Tian Xing)MR#01k:05153
	86.	The Minimum Norm of Solutions of a Boolean Matrix Equation A^k=J, Graph Theory Notes of New York XXXVIII (2000) 7--11. ( with Miao Zhengke) MR#00k:15035
	87.	The Broadcast Function Value B(23) is 33 or 34, Acta Mathematicae Applicatae Sinica 16(3) (2000) 329--331. (with Lu Chang Hong) MR#:1779027
	88.	On (d,2)-dominating Number of Biniary Undirected de Bruijn Graphs, Discrete Applied Mathematics 105 (2000) 137--145. (with Lu Chang Hong and Xu Junming) MR#01g:05076
	89.	The Minimal Solutions of Boolean Matrix Equation A^k=J, Northeastern Mathematical Journal, 16(2) (2000) 155--159. (with Maio Zhengke)MR#01m:15038
	90.	On the Ramsey number R(C_n or K_n-1, K_m)(n=3,4), Australasian J. of Combinatorics 22 (2000) 307--311. (with Yang Jian Sheng and Huang Yi Ru) MR#01f:05099
	91.	Ramsey Theory, Mathematical Dissemination Quarterly 24(4) (2000) 35--44.
	92.	Outpaths of Arcs in Multipartite Tournaments, Acta Mathematicae Applicatae Sinica 17(3) (2001) 361--365. (with Zhou Guofei) MR#02j:05078
	93.	A Note on List Improper Coloring Planar Graphs, Applied Mathematics Letters 14(3) (2001) 269--273. (with Ko-wei Lih, Song Zeng Min and Wang Wei Fan) MR#05k:05075
	94.	A Minimum Broadcast Graphs on 26 Vertices, Applied Mathematics Letters 14(8) (2001) 1023--1026. (with Zhou Jianguo) MR#02f:05098
	95.	R(C₆,K₅)=21 and R(C₇,K₅)=25, European J. of Combinatorics 22(4) (2001) 561--567. (with Yang Jian Sheng and Huang Yi Ru) MR#02a:05182
	96.	The Generalized Maximum Density Index Sets of Primitive Matrices with d Nonzero Diagonal Entries, Acta Mathematicae Sinica 44(1) (2001) 15--20. (with Miao Zhengke and Pan Lin Qiang) MR#01m:15043
	97.	A Bound for Multicolor Ramsey Numbers, Discrete Mathematics 226 (2001) 419--421. (with Shi Ling Sheng) MR#01i:05108
	98.	On Score Sequence of k-hypertournaments, Chinese Annals of Mathematics A22(1) (2001) 115--120 or Chinese Journal of Contemporary Mathematics 22(1) (2001) 95--102. (with Zhou Guofei) MR#02b:05070
	99.	(d,2n)-dominating Number of the Toroidal Mesh C(d₁, d₂,...,d_n) with Diameter d, Chinese Annals of Mathematics 22(4) A (2001) 517--524 or Chinese Journal of Contemporary Mathematics 22(3) (2001) 299--306. (with Lu Chang Hong) MR#02d:05093
	100.	Vertex Pancyclic Mnltipartite Tournaments, Journal of Nanjing University 37(4) (2001) 477--485. (with Zhou Guo Fei and Xue Guohe) MR#02i:05058
	101.	A Seven Color Theorem on the Edge-face Coloring of Plane Graphs, Acta Mathematicae Applicatae Sinica 21(2) (2001) 243--248. (with Wang Wei Fan)MR#02b:05064
	102.	An Ore-type Condition for Cyclability, European J. of Combinatorics 22 (2001) 953--960. (with Chen Yaojun and Zhang Yunqing) MR#02g:05116
	103.	Edge-pancyclicity of Coupled Graph, Discrete Applied Mathematics 119 (2002)259--264.(with Ko-wei Lih, Song Zeng Min and Wang Wei Fan)MR#03d:05117
	104.	Cycles Containing a Given Arc in Regular Multipartite Tournaments, Acta Mathematicae Applicatae Sinica 18(4) (2002) 681--684. (with Zhou Guo Fei) MR#04h:05060
	105.	Vertex Pancyclicity in Almost Regular Multipartite Tournaments, Chinese Annals of Mathematics A23(5) (2002) 585--596 oror Chinese Journal of Contemporary Mathematics 23(4) (2002) (with Pan Lin Qiang)MR#03k:05061
	106.	On Container Length And Wide-diameter in Unidirectional Hypercubes, Taiwanese J. of Mathematics 6(1)(2002) 75--87. (with Lu Chang Hong)MR#03a:68108
	107.	A Note on Reducible Cycle in Multipartite Tournaments, Taiwanese J. of Mathematics 6(2)(2002) 235--239. (with Pan Ling-Qiang Miao Zheng-Ke)MR#03b:05077
	108.	(d,m)-dominating Numbers of Hypercubes,Applied Mathematics---A J. of Chinese Universities B17(1) (2002) 105--108. (with Lu Chang Hong)MR#03a:05113
	109.	(1)Hypergraphs (A chinese translation of C Berge's book), (2)The Solutions of Exercise in Hypergraphs, The Southeast University Press (2002) (with Bu Yue Hua)
	110.	Super Connectivity and Restricted Connectivity of Undirected de Bruijn Graphs, Acta Mathematicae Applicatae Sinica 25(1) (2002) 29--35. (with Lu Chang Hong) MR#03g:05083
	111.	On tournaments with Small Order And Their Applications, Journal of Systems Science and Complexity 16(4) (2003) 475--482. (with Zhou Guo Fei) MR#:2013900
	112.	Is γ_α≤δ Graphs Which Have Diameter Two? Journal of Systems Science and Complexity 16 (2003) 195--198.(with Chen Yaojun and Zhang Yunqing) MR#04c:05136
	113.	c -Pancyclic Partial Ordering and (c-1)-Pan-Outpaths Partial Ordering in Semicomplete Multipartite Digraphs, Acta Mathematicae Sinica 19(4) (2003) 829--832. (with Pan Lin Qiang) MR#04i:05065
	114.	Upper Bounds for Ramsey Numbers R(m,n,l) And R(m,n,l.s) with Parameter, Journal of Shanghai University 7(1)(2003) 46--48. (with Huang Yi Ru and Yue Hong) MR#:1964492
	115.	The Ramsey Numbers of Stars Versus Wheels,European J. of Combinatorics25(7) (2004) 1067--1075.(with Chen Yaojun and Zhang Yunqing) MR#05e:05094
	116.	On Cycles Containing a Given Arc in Regular Multipartite Tournaments, Acta Mathematicae Sinica 22(2) (2004) 379--394. (with Pan Lin Qiang) MR#05a:05105
	117.	The Ramsey Numbers R(T_n,W₆) for Δ(T_n)≥n-3, Applied Mathematics Letters 17 (2004) 281--285. (with Chen Yaojun and Zhang Yunqing)MR#:2044037
	118.	The Ramsey numbers for R(T_n,W₆) for T_n without certain deletable sets,Journal of Systems Science and Complexity, 18(1) (2005) 95--101. (with Chen Yaojun and Zhang Yunqing) MR#:2123040
	119.	The Ramsey Numbers of Paths Versus Wheels, Discrete Mathematics 290(2005) 85--87. (with Chen Yaojun and Zhang Yunqing) MR#05h:05134
	120.	The Ramsey Numbers R(T_n,W₆) for Small n, Utilitas Mathematica 67(2005) 269--284. (with Chen Yaojun and Zhang Yunqing) MR#05k:05159
	121.	Entirechromatic number and Δ-matching of outerplane graphs, Acta Mathematica Scientia 25B(4)(2005) 672--680. (with Wang Weifan) MR#:07b:05084
	122.	The Ramsey Number for Stars and Stripes, Acta Mathematica Scientia 25(4) (2005) 1067-1072. (with Zhang Shu Sheng) MR#06m:05163
	123.	The Ramsey numbers of trees versus W₆ or W₇, European J. of Combinatorics 27 (2006) 558-564. (with Chen Yaojun and Zhang Yunqing) MR#06m:05162
	124.	A Note on Ramsey Numbers with Two Parameters, European J. of Combinatorics 27 (2006) 574-576. (with Huang Yi Ru and Yang Jian Sheng) MR# 06j:05136
	125.	New Upper Bound Formulas with Parameters for Ramsey Numbers, Discrete Mathematics 307(6) (2006) 760--763. (with Huang Yiru, Wang Yuandi, Sheng Wancheng, Yang Jiansheng, Huang Jian) MR#07h:05106
	126.	Progress of Some Problems in Graph Theory, J.of Mathematical Research and Exposition 27(3)(2007) 563--576. MR2349503
	127.	The Ramsey Number for stars of even order versus a wheel of order nine, European J. of Combinatorics (2008) (with Chen Yaojun and Zhang Yunqing) MR#09e:05024
	128.	The Ramsey Number $R(C_8,K_8)$, Discrete Mathematics 309 (2009) (with Zhang Yunqing) MR#10g:05246