## Haihui Zhang

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

Comment.Math.Univ.Carolin. 54,3 (2013) 339-344.**Abstract:**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.

**Keywords:** toroidal graph; defective choosability; chord

**AMS Subject Classification:** 05C15 05C78

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