Geodesic
On $(4,1)^*$-choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 339-344

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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.
Classification : 05C15, 05C78
Keywords: toroidal graph; defective choosability; chord 
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Zhang, Haihui. On $(4,1)^*$-choosability of toroidal graphs without chordal 7-cycles and adjacent 4-cycles. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 339-344. http://geodesic.mathdoc.fr/item/CMUC_2013__54_3_a2/