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- W4287214851 abstract "A famous result by Rodl, Ruci'nski, and Szemer'edi guarantees a (tight) Hamilton cycle in $k$-uniform hypergraphs $H$ on $n$ vertices with minimum $(k-1)$-degree $delta_{k-1}(H)geq (1/2+o(1))n$, thereby extending Dirac's result from graphs to hypergraphs. For graphs, much more is known; each graph on $n$ vertices with $delta(G)geq (1/2+o(1))n$ contains $(1-o(1))r$ edge-disjoint Hamilton cycles where $r$ is the largest integer such that $G$ contains a spanning $2r$-regular subgraph, which is clearly asymptotically optimal. This was proved by Ferber, Krivelevich, and Sudakov answering a question raised by Kuhn, Lapinskas, and Osthus. We extend this result to hypergraphs; every $k$-uniform hypergraph $H$ on $n$ vertices with $delta_{k-1}(H)geq (1/2+o(1))n$ contains $(1-o(1))r$ edge-disjoint (tight) Hamilton cycles where $r$ is the largest integer such that $H$ contains a spanning subgraph with each vertex belonging to $kr$ edges. In particular, this yields an asymptotic solution to a question of Glock, Kuhn, and Osthus. In fact, our main result applies to approximately vertex-regular $k$-uniform hypergraphs with a weak quasirandom property and provides approximate decompositions into cycle factors without too short cycles." @default.
- W4287214851 created "2022-07-25" @default.
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- W4287214851 date "2021-04-13" @default.
- W4287214851 modified "2023-09-30" @default.
- W4287214851 title "Decomposing hypergraphs into cycle factors" @default.
- W4287214851 doi "https://doi.org/10.48550/arxiv.2104.06333" @default.
- W4287214851 hasPublicationYear "2021" @default.
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