Spectral radius and perfect k-matchings in t-connected graphs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913094671794176 |
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| author | Pan, Quanru Zhou, Sizhong |
| author_facet | Pan, Quanru Zhou, Sizhong |
| contents | A $k$-matching of a graph $G$ is a function $f:E(G)\rightarrow\{0,1,2,\ldots,k\}$ with $\sum\limits_{e\in E_G(v)}f(e)\leq k$ for each vertex $v$ of $G$, where $E_G(v)$ is the set of edges incident with $v$ in $G$. A perfect $k$-matching of a graph $G$ is a $k$-matching $f$ satisfying $\sum\limits_{e\in E_G(v)}f(e)=k$ for any vertex $v$ of $G$. A fractional perfect matching of a graph $G$ is a function $f:E(G)\rightarrow [0,1]$ satisfying $\sum\limits_{e\in E_G(v)}f(e)=1$ for any $v\in V(G)$. We denote by $ρ(G)$ the spectral radius of $G$. In this paper, we put forward a tight spectral radius condition for a $t$-connected graph to possess a perfect $k$-matching and a tight spectral radius condition for the existence of a perfect $k$-matching in a $t$-connected graph with a fractional perfect matching. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04876 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral radius and perfect k-matchings in t-connected graphs Pan, Quanru Zhou, Sizhong Combinatorics 05C50, 05C70 A $k$-matching of a graph $G$ is a function $f:E(G)\rightarrow\{0,1,2,\ldots,k\}$ with $\sum\limits_{e\in E_G(v)}f(e)\leq k$ for each vertex $v$ of $G$, where $E_G(v)$ is the set of edges incident with $v$ in $G$. A perfect $k$-matching of a graph $G$ is a $k$-matching $f$ satisfying $\sum\limits_{e\in E_G(v)}f(e)=k$ for any vertex $v$ of $G$. A fractional perfect matching of a graph $G$ is a function $f:E(G)\rightarrow [0,1]$ satisfying $\sum\limits_{e\in E_G(v)}f(e)=1$ for any $v\in V(G)$. We denote by $ρ(G)$ the spectral radius of $G$. In this paper, we put forward a tight spectral radius condition for a $t$-connected graph to possess a perfect $k$-matching and a tight spectral radius condition for the existence of a perfect $k$-matching in a $t$-connected graph with a fractional perfect matching. |
| title | Spectral radius and perfect k-matchings in t-connected graphs |
| topic | Combinatorics 05C50, 05C70 |
| url | https://arxiv.org/abs/2605.04876 |