Two conjectures on edge-colouring

Abstract Chetwynd and Hilton have elsewhere posed two conjectures, one a general statement on edge-colouring simple graphs G with Δ(G) > 1 3 ∣V(G)∣ , and a second to the effect that a regular simple graph G with d(G) ⩾ 1 2 ∣V(G)∣ is 1-factorizable. We set out the evidence for both these conjectures and show that the first implies the second.

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