The list chromatic index of simple graphs whose odd cycles intersect in at most one edge

We study the class of simple graphs g* for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in g* and prove that every G is an element of g* satisfies the list-edge-coloring conjecture. When Delta(G) >= 4, we in fact prove a stronger result about kernel-perfect orientations in L(G) which implies that G is (m Delta(G) : m)-edge-choosable and Delta(G)-edge-paintable for every m >= 1. (C) 2017 Elsevier B.V. All rights reserved.