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A Conjecture on Rainbow Hamiltonian Cycle Decomposition
- Publication Year :
- 2024
-
Abstract
- 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.
- Subjects :
- Mathematics - Combinatorics
05C70, 05C38
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.17290
- Document Type :
- Working Paper