2024/01/31 by Yuke Zhang, Edwin van Dam, Zhang, Yuke +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2401.17845
openalex publication_date 2024/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=\G1,…,Gn \ be a family of graphs of order n with the same vertex set. A rainbow Hamiltonian cycle in G is a cycle that visits each vertex precisely once such that any two edges belong to different graphs of G. We show that if each Gi has more than \binomn-12+1 edges, then G admits a rainbow Hamiltonian cycle and pose the problem of characterizing rainbow Hamiltonicity under the condition that all Gi have at least \binomn-12+1 edges. Towards a solution of that problem, we give a sufficient condition for the existence of a rainbow Hamiltonian cycle in terms of the spectral radii of the graphs in G and completely characterize the corresponding extremal graphs.