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- W2989452715 abstract "The anti-Ramsey problem was introduced by ErdH{o}s, Simonovits and S'{o}s in 1970s. The anti-Ramsey number of a hypergraph $mathcal{H}$, $ar(n,s, mathcal{H})$, is the smallest integer $c$ such that in any coloring of the edges of the $s$-uniform complete hypergraph on $n$ vertices with exactly $c$ colors, there is a copy of $mathcal{H}$ whose edges have distinct colors. In this paper, we determine the anti-Ramsey numbers of linear paths and loose paths in hypergraphs for sufficiently large $n$, and give bounds for the anti-Ramsey numbers of Berge paths. Similar exact anti-Ramsey numbers are obtained for linear/loose cycles, and bounds are obtained for Berge cycles. Our main tools are path extension technique and stability results on hypergraph Tur'{a}n problems of paths and cycles." @default.
- W2989452715 created "2019-11-22" @default.
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- W2989452715 date "2019-01-18" @default.
- W2989452715 modified "2023-09-24" @default.
- W2989452715 title "Anti-Ramsey numbers of paths and cycles in hypergraphs" @default.
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- W2989452715 doi "https://doi.org/10.48550/arxiv.1901.06092" @default.
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