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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.04379 |
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| _version_ | 1866914305441529856 |
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| author | Bai, Xiyan Wang, Tao Yang, Mengke Yang, Xiaojing |
| author_facet | Bai, Xiyan Wang, Tao Yang, Mengke Yang, Xiaojing |
| contents | A fractional matching of a graph $G$ is a function $h: E(G) \to [0,1]$ such that $\sum_{e \in E_G(v)} h(e) \leq 1$ for every vertex $v \in V(G)$, where $E_G(v)$ is the set of edges incident to $v$. If $\sum_{e \in E_G(v)} h(e) = 1$ for all $v$, then $h$ is a fractional perfect matching. A graph $G$ is fractional $k$-extendable if it has a matching of size $k$ and every $k$-matching $M$ in $G$ is contained in a fractional perfect matching $h$ such that $h(e)=1$ for every $e \in M$. In this paper, we establish new sufficient conditions for a graph with minimum degree $δ$ to be fractional $k$-extendable. Our main results provide spectral guarantees for this property based on the distance spectral radius and the signless Laplacian spectral radius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04379 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On spectral conditions for fractional $k$-extendable graphs Bai, Xiyan Wang, Tao Yang, Mengke Yang, Xiaojing Combinatorics A fractional matching of a graph $G$ is a function $h: E(G) \to [0,1]$ such that $\sum_{e \in E_G(v)} h(e) \leq 1$ for every vertex $v \in V(G)$, where $E_G(v)$ is the set of edges incident to $v$. If $\sum_{e \in E_G(v)} h(e) = 1$ for all $v$, then $h$ is a fractional perfect matching. A graph $G$ is fractional $k$-extendable if it has a matching of size $k$ and every $k$-matching $M$ in $G$ is contained in a fractional perfect matching $h$ such that $h(e)=1$ for every $e \in M$. In this paper, we establish new sufficient conditions for a graph with minimum degree $δ$ to be fractional $k$-extendable. Our main results provide spectral guarantees for this property based on the distance spectral radius and the signless Laplacian spectral radius. |
| title | On spectral conditions for fractional $k$-extendable graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.04379 |