Abstract
In a graph G of maximum degree Δ, let γ denote the largest fraction of edges that can be Δ-edge-colored. This paper investigates lower bounds for γ together with infinite families of graphs in which γ is bounded away from 1. For instance, if G is cubic, then γ ⩾ 13 15 ; and there exists an infinite family of 3-connected cubic graphs in which γ ⩽ 25 27 .
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