Eigenvalue conditions implying edge-disjoint spanning trees and a forest with constraints

Fuente: arXiv
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Main Authors: Cai, Jin, Zhou, Bo
Format: Preprint
Published: 2025
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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