List edge and list total colorings of planar graphs without 4-cycles

Authors:
Jianfeng Hou;Guizhen Liu;Jiansheng Cai
Affiliations:
Department of Mathematics, School of Mathematics and System Sciences, Shandong University, Jinan, PR China;Department of Mathematics, School of Mathematics and System Sciences, Shandong University, Jinan, PR China;Department of Mathematics, School of Mathematics and System Sciences, Shandong University, Jinan, PR China
Venue:
Theoretical Computer Science
Year:
2006

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Abstract

Let G be a planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the list chromatic index χ′1(G) = Δ and the list total chromatic number χ″1(G) = Δ + 1 if (Δ, k) ∈ {(7, 4), (6, 5), (5, 8)}. Furthermore, χ′1(G) = Δ if (Δ, k) ∈ {(4, 14)}.