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

Haihui Zhang — 2013

Commentationes Mathematicae Universitatis Carolinae

A graph G is called ( k , d ) * -choosable if for every list assignment L satisfying | L ( v ) | = k for all v 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.

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