Edge choosability and total choosability of planar graphs with no 3-cycles adjacent 4-cycles
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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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.06.031