Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles
نویسندگان
چکیده
منابع مشابه
Edge-choosability and total-choosability of planar graphs with no adjacent 3-cycles
Let G be a planar graph with no two 3-cycles sharing an edge. We show that if ∆(G) ≥ 9, then χ′l(G) = ∆(G) and χ ′′ l (G) = ∆(G) + 1. We also show that if ∆(G) ≥ 6, then χ ′ l(G) ≤ ∆(G) + 1 and if ∆(G) ≥ 7, then χ′′ l (G) ≤ ∆(G) + 2. All of these results extend to graphs in the projective plane and when ∆(G) ≥ 7 the results also extend to graphs in the torus and Klein bottle. This second edge-c...
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We show that if G is a planar graph with no two 3-faces sharing an edge and with ∆(G) 6= 5, then G is (∆(G) + 1)-edge-choosable. This improves results of Wang and Lih and of Zhang and Wu. We also show that if G is a planar graph with ∆(G) = 5 and G has no 4-cycles, then G is 6-edge-choosable. In addition, we prove that if G is a planar graph with ∆(G) = 5 and the distance between any two 3-face...
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In this paper, we aim to introduce the group version of edge coloring and list edge coloring, and prove that all 2-degenerate graphs along with some planar graphs without adjacent short cycles is group (∆(G) + 1)-edgechoosable while some planar graphs with large girth and maximum degree is group ∆(G)-edge-choosable.
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Let χl (G), χ ′ l (G), χ ′′ l (G), and 1(G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. (1) 2 ≤ χl (G) ≤ 3 and χl (G) = 2 if and only if G is bipartite with at most one cycle. (2) 1(G) ≤ χ ′ l (G) ≤ 1(G) + 1 and χ ′ l (G) = 1(G) + ...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2009
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1438