On $(4,1)^*$-choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles

Commentationes mathematicae Universitatis Carolinae

Haihui Zhang¹ 

关键词: toroidal graph;    defective choosability;    chord;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

A graph $G$ is called $(k,d)^*$-choosable if for every list assignment $L$ satisfying $|L(v)|= k$ for all $v\in V(G)$, there is an $L$-coloring of $G$ such that each vertex of $G$ has at most $d$ neighbors colored with the same color as itself. In this paper, it is proved that every toroidal graph without chordal 7-cycles and adjacent 4-cycles is $(4,1)^*$-choosable.

【 授权许可】

CC BY