Spectral radius and rainbow $k$-factors in a bipartite graph family
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911528990539776 |
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| author | Chen, Meng Liu, Ruifang |
| author_facet | Chen, Meng Liu, Ruifang |
| contents | Let $\mathcal{G}=\{G_1, G_2, \ldots , G_{kn}\}$ be a family of balanced bipartite graphs on the same vertex set $[2n]$. A rainbow $k$-factor of $\mathcal{G}$ is defined as a $k$-factor such that any two distinct edges come from different graphs in $\mathcal{G}.$ In this paper, we provide a tight sufficient condition in terms of the spectral radius for a family of balanced bipartite graphs $\mathcal{G}$ to contain a rainbow $k$-factor. Furthermore, we completely characterize the corresponding spectral extremal graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18517 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral radius and rainbow $k$-factors in a bipartite graph family Chen, Meng Liu, Ruifang Combinatorics Let $\mathcal{G}=\{G_1, G_2, \ldots , G_{kn}\}$ be a family of balanced bipartite graphs on the same vertex set $[2n]$. A rainbow $k$-factor of $\mathcal{G}$ is defined as a $k$-factor such that any two distinct edges come from different graphs in $\mathcal{G}.$ In this paper, we provide a tight sufficient condition in terms of the spectral radius for a family of balanced bipartite graphs $\mathcal{G}$ to contain a rainbow $k$-factor. Furthermore, we completely characterize the corresponding spectral extremal graph. |
| title | Spectral radius and rainbow $k$-factors in a bipartite graph family |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.18517 |