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List edge and list total colorings of planar graphs without non-induced 7-cycles

Abstract : Giving a planar graph G, let χ'l(G) and χ''l(G) denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if G is a planar graph without non-induced 7-cycles, then χ'l(G)≤Δ(G)+1 and χ''l(G)≤Δ(G)+2 where Δ(G)≥7.
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Aijun Dong, Guizhen Liu, Guojun Li. List edge and list total colorings of planar graphs without non-induced 7-cycles. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 1 (1), pp.101--106. ⟨hal-00990609⟩

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