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- W2270656870 abstract "Let $k ge 3$ be an integer, $H_{k}(G)$ be the set of vertices of degree at least $2k$ in a graph $G$, and $L_{k}(G)$ be the set of vertices of degree at most $2k-2$ in $G$. In 1963, Dirac and ErdH{o}s proved that $G$ contains $k$ (vertex-)disjoint cycles whenever $|H_{k}(G)| - |L_{k}(G)| ge k^{2} + 2k - 4$. The main result of this paper is that for $k ge 2$, every graph $G$ with $|V(G)| ge 3k$ containing at most $t$ disjoint triangles and with $|H_{k}(G)| - |L_{k}(G)| ge 2k + t$ contains $k$ disjoint cycles. This yields that if $k ge 2$ and $|H_{k}(G)| - |L_{k}(G)| ge 3k$, then $G$ contains $k$ disjoint cycles. This generalizes the Corr'{a}di-Hajnal Theorem, which states that every graph $G$ with $H_{k}(G) = V(G)$ and $|H_{k}(G)| ge 3k$ contains $k$ disjoint cycles." @default.
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- W2270656870 date "2016-02-08" @default.
- W2270656870 modified "2023-09-27" @default.
- W2270656870 title "Strengthening theorems of Dirac and ErdH{o}s on disjoint cycles" @default.
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