Spectral radius and rainbow Hamiltonicity in bipartite graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914368264863744 |
|---|---|
| author | chen, Meng Liu, Ruifang Yuan, Qixuan |
| author_facet | chen, Meng Liu, Ruifang Yuan, Qixuan |
| contents | Let $\mathcal{G}=\{G_1, G_2, \ldots , G_k\}$ be a family of bipartite graphs on the same vertex set. A rainbow Hamilton path (cycle) in $\mathcal{G}$ is a path (cycle) that visits each vertex precisely once such that any two edges belong to different graphs of $\mathcal{G}.$ In this paper, by adopting the technique of bi-shifting, we present tight sufficient conditions in terms of the spectral radius for a family $\mathcal{G}$ to admit a rainbow Hamilton path and cycle, respectively. Meanwhile, we completely characterize the corresponding spectral extremal graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03966 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral radius and rainbow Hamiltonicity in bipartite graphs chen, Meng Liu, Ruifang Yuan, Qixuan Combinatorics 05C50, 05C35 Let $\mathcal{G}=\{G_1, G_2, \ldots , G_k\}$ be a family of bipartite graphs on the same vertex set. A rainbow Hamilton path (cycle) in $\mathcal{G}$ is a path (cycle) that visits each vertex precisely once such that any two edges belong to different graphs of $\mathcal{G}.$ In this paper, by adopting the technique of bi-shifting, we present tight sufficient conditions in terms of the spectral radius for a family $\mathcal{G}$ to admit a rainbow Hamilton path and cycle, respectively. Meanwhile, we completely characterize the corresponding spectral extremal graphs. |
| title | Spectral radius and rainbow Hamiltonicity in bipartite graphs |
| topic | Combinatorics 05C50, 05C35 |
| url | https://arxiv.org/abs/2603.03966 |