A Conjecture on Rainbow Hamiltonian Cycle Decomposition
arxiv(2024)
摘要
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)|≤ n+1, H is a linear forest, or n≤ 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.
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