科研之友
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摘要
An (L,d)*-coloring is a mapping phi that assigns a color phi(v) is an element of L(v) to each vertex v is an element of V(G) such that at most d neighbors of v receive colore phi(v). A graph is called (m, d)*-choosable, if G admits an (L,d)*-coloring for every list assignment L with vertical bar L(v)vertical bar >= m for all v is an element of V(G). In this note, it is proved that every toroidal graph, which contains no adjacent triangles and contains no 6-cycles and l-cycles for some l is an element of {5, 7}, is (3, 1)*-choosable.
