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