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- W2253939070 abstract "In 2000, Enomoto and Ota conjectured that if a graph $G$ satisfies $sigma_{2}(G) geq n + k - 1$, then for any set of $k$ vertices $v_{1}, dots, v_{k}$ and for any positive integers $n_{1}, dots, n_{k}$ with $sum n_{i} = |G|$, there exists a partition of $V(G)$ into $k$ paths $P_{1}, dots, P_{k}$ such that $v_{i}$ is an end of $P_{i}$ and $|P_{i}| = n_{i}$ for all $i$. We prove this conjecture when $|G|$ is large. Our proof uses the Regularity Lemma along with several extremal lemmas, concluding with an absorbing argument to retrieve misbehaving vertices." @default.
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- W2253939070 date "2014-08-02" @default.
- W2253939070 modified "2023-09-24" @default.
- W2253939070 title "Enomoto and Ota's conjecture holds for large graphs" @default.
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