List-edge-coloring of planar graphs without 6-cycles with three chords

Haiying Wang () and Jianliang Wu ()
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Haiying Wang: China University of Geosciences (Beijing)
Jianliang Wu: Shandong University

Journal of Combinatorial Optimization, 2018, vol. 35, issue 2, No 17, 555-562

Abstract: Abstract A graph G is edge-k-choosable if, whenever we are given a list L(e) of colors with $$|L(e)|\ge k$$ | L ( e ) | ≥ k for each $$e\in E(G)$$ e ∈ E ( G ) , we can choose a color from L(e) for each edge e such that no two adjacent edges receive the same color. In this paper we prove that if G is a planar graph, and each 6-cycle contains at most two chords, then G is edge-k-choosable, where $$k=\max \{8,\Delta (G)+1\}$$ k = max { 8 , Δ ( G ) + 1 } , and edge-t-choosable, where $$t=\max \{10,\Delta (G)\}$$ t = max { 10 , Δ ( G ) } .

Keywords: Edge-choosable; List-edge-chromatic-number; Cycle; Planar graph (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0193-2

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