A Conjecture on Rainbow Hamiltonian Cycle Decomposition
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917622131458048 |
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| author | Javadi, Ramin Miralaei, Meysam |
| author_facet | Javadi, Ramin Miralaei, Meysam |
| contents | Wu in 1999 conjectured that if $H$ is a subgraph of the complete graph $K_{2n+1}$ with $n$ edges, then there is a Hamiltonian cycle decomposition of $K_{2n+1}$ such that each edge of $H$ is in a separate Hamiltonian cycle. The conjecture was partially settled by Liu and Chen (2023) in cases that $|V(H)|\leq n+1$, $H$ is a linear forest, or $n\leq 5$. In this paper, we settle the conjecture completely. This result can be viewed as a complete graph analogous of Evans conjecture and has some applications in linear arboricity conjecture and restricted size Ramsey numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17290 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Conjecture on Rainbow Hamiltonian Cycle Decomposition Javadi, Ramin Miralaei, Meysam Combinatorics 05C70, 05C38 Wu in 1999 conjectured that if $H$ is a subgraph of the complete graph $K_{2n+1}$ with $n$ edges, then there is a Hamiltonian cycle decomposition of $K_{2n+1}$ such that each edge of $H$ is in a separate Hamiltonian cycle. The conjecture was partially settled by Liu and Chen (2023) in cases that $|V(H)|\leq n+1$, $H$ is a linear forest, or $n\leq 5$. In this paper, we settle the conjecture completely. This result can be viewed as a complete graph analogous of Evans conjecture and has some applications in linear arboricity conjecture and restricted size Ramsey numbers. |
| title | A Conjecture on Rainbow Hamiltonian Cycle Decomposition |
| topic | Combinatorics 05C70, 05C38 |
| url | https://arxiv.org/abs/2403.17290 |