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arXiv · 2511.13004

The existence of even factors based on spectral conditions of graphs

Jiasheng Li·Xiaoyun Lv·Shoujun Xu
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Abstract

Let $G=(V(G),E(G)) $ be a graph with vertex set $V(G)$ and edge set $E(G)$. An even factor of $G$ is a spanning subgraph $F$ such that every vertex in $F$ has a nonzero even degree. Note that $\delta(G)\geq 2$ is a trivial necessary condition for a graph to have an even factor, where \( \delta(G) \) is the minimum degree of \( G \). In this paper, for a connected graph $G$ with minimum degree $\delta$, we establish a lower bound on the signless Laplacian spectral radius of $G$ and an upper bound on the distance spectral radius of $G$ such that $G$ contains an even factor.

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Jiasheng Li, Xiaoyun Lv, Shoujun Xu. 2025-11-17. The existence of even factors based on spectral conditions of graphs. https://arxiv.org/abs/2511.13004

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