Eigenvalues, edge-disjoint perfect matchings and toughness of regular graphs
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| Title: | Eigenvalues, edge-disjoint perfect matchings and toughness of regular graphs |
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| Authors: | Wenqian Zhang |
| Source: | Linear Algebra and its Applications. 726:359-370 |
| Publication Status: | Preprint |
| Publisher Information: | Elsevier BV, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO) |
| Description: | Let $G$ be a connected $d$-regular graph of order $n$, where $d\geq3$. Let $λ_{2}(G)$ be the second largest eigenvalue of $G$. For even $n$, we show that $G$ contains $\left\lfloor\frac{2}{3}(d-λ_{2}(G))\right\rfloor$ edge-disjoint perfect matchings. This improves a result stated by Cioabă, Gregory and Haemers \cite{CGH}. Let $t(G)$ be the toughness of $G$. When $G$ is non-bipartite, we give a sharp upper bound of $λ_{2}(G)$ to guarantee that $t(G)>1$. This enriches the previous results on this direction. |
| Document Type: | Article |
| Language: | English |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2025.07.033 |
| DOI: | 10.48550/arxiv.2410.04413 |
| Access URL: | http://arxiv.org/abs/2410.04413 |
| Rights: | Elsevier TDM CC BY |
| Accession Number: | edsair.doi.dedup.....748600612e9f02914f9380f6515aae83 |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | Let $G$ be a connected $d$-regular graph of order $n$, where $d\geq3$. Let $λ_{2}(G)$ be the second largest eigenvalue of $G$. For even $n$, we show that $G$ contains $\left\lfloor\frac{2}{3}(d-λ_{2}(G))\right\rfloor$ edge-disjoint perfect matchings. This improves a result stated by Cioabă, Gregory and Haemers \cite{CGH}. Let $t(G)$ be the toughness of $G$. When $G$ is non-bipartite, we give a sharp upper bound of $λ_{2}(G)$ to guarantee that $t(G)>1$. This enriches the previous results on this direction. |
|---|---|
| ISSN: | 00243795 |
| DOI: | 10.1016/j.laa.2025.07.033 |