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- W4221094607 abstract "The 1-Factorization Conjecture states that any regular graph of even order n in which the vertex degrees are at least n2 has a factorization of its edges into perfect matchings. Chetwynd and Hilton [1], [3] and independently Niessen and Volkmann [11] verified this conjecture when the vertex degrees are at least .83n. This is equivalent to saying that any such regular graph G has chromatic index χ′(G) equal to its maximum degree Δ(G). Using that result, it was shown in [14] that for any graph G (not necessarily regular) of even order n and minimum degree at least .882n, χ′(G)=Δ(G) if and only if there is no vertex v for which the number of edges of G−v surpasses Δ(G)⋅(n2−1). Recently, Csaba, Kühn, Lo, Osthus and Treglown [6] verified that the 1-Factorization Conjecture holds for all graphs with sufficiently large n. Using this result, we show that for any graph with even order n sufficiently large and minimum degree at least 2n3,χ′(G)=Δ(G) if and only if no vertex-deleted subgraph has more than Δ(G)⋅(n2−1) edges. These results are presented in the context of the more general Overfull Conjecture." @default.
- W4221094607 created "2022-04-03" @default.
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- W4221094607 date "2022-07-01" @default.
- W4221094607 modified "2023-10-15" @default.
- W4221094607 title "The chromatic index of graphs with large even order n and minimum degree at least 2n/3" @default.
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- W4221094607 doi "https://doi.org/10.1016/j.disc.2022.112880" @default.
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