Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423591 | Discrete Mathematics | 2011 | 6 Pages |
Two cycles are said to be adjacent if they share a common edge. Let G be a planar graph without triangles adjacent 4-cycles. We prove that Ïlâ³(G)â¤Î(G)+2 if Î(G)â¥6, and Ïlâ²(G)=Î(G) and Ïlâ³(G)=Î(G)+1 if Î(G)â¥8, where Ïlâ²(G) and Ïlâ³(G) denote the list edge chromatic number and list total chromatic number of G, respectively.
⺠The list edge colorings and list total colorings of planar graphs without triangles adjacent 4-cycles are investigated. ⺠We proved that, if a planar graph G without triangles adjacent 4-cycles and Î(G)â¥8, then Ïlâ²(G)=Î(G). ⺠It is proved that Ïlâ³(G)â¤Î(G)+2, where G is a planar graph without triangles adjacent 4-cycles and Î(G)â¥6. ⺠It is proved that Ïlâ³(G)=Î(G)+1, where G is a planar graph without triangles adjacent 4-cycles and Î(G)â¥8.