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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.03554 |
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Sommario:
- A connected graph $G$ with a perfect matching is said to be $k$-extendable for integers $k$, $1 \leq k\leq \frac{|V(G)|}{2}-1$, if any matching in $G$ of size $k$ is contained in a perfect matching of $G$. A $k$-extendable graph is minimal if the deletion of any edge results in a graph that is not $k$-extendable. In 1994, Plummer proved that every $k$-extendable claw-free graph has minimum degree at least $2k$. Recently, He et al. showed that every minimal 1-extendable graph has minimum degree 2 or 3. In this paper, we prove that the minimum degree of a minimal 2-extendable claw-free graph is either $4$ or $5$.