Abstract

In this paper, we give some new results on strong list edge coloring of subcubic graphs. We prove that every subcubic graph with maximum average degree less than 52, 83 and 145 can be strongly list edge colored with seven, eight and nine colors respectively.

Highlights

  • All graphs in this paper are finite and simple

  • We study strong list edge coloring of subcubic graphs, and we prove that every subcubic graph with maximum average degree less than 15/7, 27/11, 13/5, and 36/13 can be strongly list edge colored with six, seven, eight, and nine colors, respectively

  • For a graph G with vertex set V(G) and edge set E(G), a proper edge coloring of G is an assignment of colors to the edges of G so that no two adjacent edges receive the same color

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Summary

Introduction

All graphs in this paper are finite and simple. For a graph G with vertex set V(G) and edge set E(G), a proper edge coloring of G is an assignment of colors to the edges of G so that no two adjacent edges receive the same color. Strong edge coloring was introduced by Fouquet and Jolivet [1, 2]. Denote by Δ the maximum degree of the graph. Let mad (G) = maxH⊆G,|V(H)|≥1(2|E(H)|/|V(H)|) be the maximum average degree of the graph G. Hocquard and Valicov [6] considered the subcubic graphs with bounded maximum average degree, and they proved the following results. For a positive integer k, a graph G is strongly k-edge choosable if for every k-edge list L, G is strongly Ledge colorable. The strong list chromatic index χl󸀠s(G) is the minimum positive integer k for which G is strongly k-edge choosable. We consider strong list edge coloring of subcubic graphs and extend Theorem 1 to the list version.

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