Improper choosability of graphs of nonnegative characteristic

Yongzhu Chen, Weiyi Zhu, Weifan Wang
2008 Computers and Mathematics with Applications  
A graph G is called (k, d) * -choosable if, for every list assignment L with |L(v)| = k for all v ∈ V (G), there is an L-coloring of G such that every vertex has at most d neighbors having the same color as itself. Let G be a graph embeddable in a surface of nonnegative characteristic. In this paper, we prove: (1) If G contains no k-cycle with a chord for all k = 4, 5, 6, then G is (3, 1) *choosable; (2) If G contains neither 5-cycle with a chord nor 6-cycle with a chord, then G is (4, 1) * -choosable.
doi:10.1016/j.camwa.2008.03.036 fatcat:437w5yexyrdplp74g6fmfvu3g4