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- W3007721824 abstract "We solve four similar problems: For every fixed $s$ and large $n$, we describe all values of $n_1,ldots,n_s$ such that for every $2$-edge-coloring of the complete $s$-partite graph $K_{n_1,ldots,n_s}$ there exists a monochromatic (i) cycle $C_{2n}$ with $2n$ vertices, (ii) cycle $C_{geq 2n}$ with at least $2n$ vertices, (iii) path $P_{2n}$ with $2n$ vertices, and (iv) path $P_{2n+1}$ with $2n+1$ vertices. This implies a generalization for large $n$ of the conjecture by Gy'arf'as, Ruszink'o, S'arkH{o}zy and Szemer'edi that for every $2$-edge-coloring of the complete $3$-partite graph $K_{n,n,n}$ there is a monochromatic path $P_{2n+1}$. An important tool is our recent stability theorem on monochromatic connected matchings." @default.
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- W3007721824 date "2020-02-20" @default.
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- W3007721824 title "Long monochromatic paths and cycles in 2-edge-colored multipartite graphs" @default.
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- W3007721824 doi "https://doi.org/10.2140/moscow.2020.9.55" @default.
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