Application of polynomial method to on-line list colouring of graphs

A graph is on-line chromatic choosable if its on-line choice number equals its chromatic number. In this paper, we consider on-line chromatic-choosable complete multi-partite graphs. Assume G is a complete k-partite graph. It is known that if the polynomial P(G) defined as P(G)=@?"u"<"v","u"v"@?"E(x"u-x"v) has one monomial @?"v"@?"Vx"v^@f^(^v^) with @f(v)

[1]  N. Alon.  Restricted colorings of graphs , 1993 .

[2]  Benny Sudakov,et al.  List Colouring When The Chromatic Number Is Close To the Order Of The Graph , 2004, Comb..

[3]  Seog-Jin Kim,et al.  On-Line List Colouring of Complete Multipartite Graphs , 2012, Electron. J. Comb..

[4]  Kyoji Ohba.  On chromatic-choosable graphs , 2002 .

[5]  Roland Häggkvist,et al.  Some upper bounds on the total and list chromatic numbers of multigraphs , 1992, J. Graph Theory.

[6]  Tommy R. Jensen,et al.  Wiley‐Interscience Series in Discrete Mathematics and Optimization , 2011 .

[7]  Zsolt Tuza,et al.  Graph colorings with local constraints - a survey , 1997, Discuss. Math. Graph Theory.

[8]  Jan Hladký,et al.  Brooks' Theorem via the Alon-Tarsi Theorem , 2010, Discret. Math..

[9]  Yufa Shen,et al.  On choosability of some complete multipartite graphs and Ohba's conjecture , 2008, Discret. Math..

[10]  Uwe Schauz,et al.  Flexible Color Lists in Alon and Tarsi's Theorem, and Time Scheduling with Unreliable Participants , 2010, Electron. J. Comb..

[11]  Sylvain Gravier,et al.  Choice number of 3-colorable elementary graphs , 1997, Discret. Math..

[12]  Tommy R. Jensen,et al.  Graph Coloring Problems , 1994 .

[13]  Eberhard Triesch,et al.  Irregular Assignments of Trees and Forests , 1990, SIAM J. Discret. Math..

[14]  Uwe Schauz,et al.  Mr. Paint and Mrs. Correct , 2009, Electron. J. Comb..

[15]  Yufa Shen,et al.  Ohba's conjecture is true for graphs with independence number at most three , 2009, Appl. Math. Lett..

[16]  Uwe Schauz,et al.  A Paintability Version of the Combinatorial Nullstellensatz, and List Colorings of k-partite k-uniform Hypergraphs , 2010, Electron. J. Comb..

[17]  Xuding Zhu,et al.  On-Line List Colouring of Graphs , 2009, Electron. J. Comb..

[18]  Fred Galvin,et al.  The List Chromatic Index of a Bipartite Multigraph , 1995, J. Comb. Theory B.

[19]  David E. Scheim,et al.  The number of edge 3-colorings of a planar cubic graph as a permanent , 1974, Discret. Math..

[20]  Kyoji Ohba.  Choice Number of Complete Multipartite Graphs with Part Size at Most Three , 2004, Ars Comb..