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- W2807728901 abstract "We study $2k$-factors in $(2r+1)$-regular graphs. Hanson, Loten, and Toft proved that every $(2r+1)$-regular graph with at most $2r$ cut-edges has a $2$-factor. We generalize their result by proving for $kle(2r+1)/3$ that every $(2r+1)$-regular graph with at most $2r-3(k-1)$ cut-edges has a $2k$-factor. Both the restriction on $k$ and the restriction on the number of cut-edges are sharp. We characterize the graphs that have exactly $2r-3(k-1)+1$ cut-edges but no $2k$-factor. For $k>(2r+1)/3$, there are graphs without cut-edges that have no $2k$-factor, as studied by Bollobas, Saito, and Wormald." @default.
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- W2807728901 date "2018-06-14" @default.
- W2807728901 modified "2023-09-26" @default.
- W2807728901 title "Cut-edges and regular factors in regular graphs of odd degree" @default.
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