Acyclic List Edge Coloring of Graphs

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Abstract

A proper edge coloring of a graph is said to be acyclic if any cycle is colored with at least three colors. An edge-list L of a graph G is a mapping that assigns a finite set of positive integers to each edge of G. An acyclic edge coloring ϕ of G such that math formula for any math formula is called an acyclic L-edge coloring of G. A graph G is said to be acyclically k-edge choosable if it has an acyclic L-edge coloring for any edge-list L that satisfies math formula for each edge e. The acyclic list chromatic index is the least integer k such that G is acyclically k-edge choosable. We develop techniques to obtain bounds for the acyclic list chromatic indices of outerplanar graphs, subcubic graphs, and subdivisions of Halin graphs.

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