Eigenvalue conditions implying edge-disjoint spanning trees and a forest with constraints
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912303281078272 |
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| author | Cai, Jin Zhou, Bo |
| author_facet | Cai, Jin Zhou, Bo |
| contents | Let $G$ be a nontrivial graph with minimum degree $δ$ and $k$ an integer with $k\ge 2$. In the literature, there are eigenvalue conditions that imply $G$ contains $k$ edge-disjoint spanning trees. We give eigenvalue conditions that imply $G$ contains $k$ edge-disjoint spanning trees and another forest $F$ with $|E(F)|>\frac{δ-1}δ(|V(G)|-1)$, and if $F$ is not a spanning tree, then $F$ has a component with at least $δ$ edges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvalue conditions implying edge-disjoint spanning trees and a forest with constraints Cai, Jin Zhou, Bo Combinatorics Let $G$ be a nontrivial graph with minimum degree $δ$ and $k$ an integer with $k\ge 2$. In the literature, there are eigenvalue conditions that imply $G$ contains $k$ edge-disjoint spanning trees. We give eigenvalue conditions that imply $G$ contains $k$ edge-disjoint spanning trees and another forest $F$ with $|E(F)|>\frac{δ-1}δ(|V(G)|-1)$, and if $F$ is not a spanning tree, then $F$ has a component with at least $δ$ edges. |
| title | Eigenvalue conditions implying edge-disjoint spanning trees and a forest with constraints |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.19461 |