Size and spectral radius conditions for the existence of k-factor in graphs with given minimum degree
Abstract
In recent years, characterizing the conditions for the existence of an [a,b]-factor in graphs has received significant academic attention. For integers b≥ a≥ 1, an $[a, b]$-factor of a graph G is defined as a spanning subgraph H such that a≤ dH(v)≤ b for every v∈ V(G). If a=b=k, a $[k, k]$-factor is called a k-factor of G. Let δ(G) denote the minimum degree of a graph G. Hao and Li [Electron. J. Combin. (2024)] posed the problem of characterizing the size or spectral radius conditions for a graph to contain an [a,b]-factor with δ(G)≥ a. Fan, Lin and Zhu [Discrete Math. (2026)] solved the size version of this problem for the case a < b. In this paper, for a=b=k, we characterize the size condition for a graph to have a k-factor with δ(G)≥ k. Using this result, we also characterize the spectral radius and distance spectral radius conditions for a graph to have a k-factor, respectively.
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BibTeX
@misc{xu2026size,
title = {{Size and spectral radius conditions for the existence of $k$-factor in graphs with given minimum degree}},
author = {Zengzhao Xu and Bo Deng and Ligong Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27783},
eprint = {2610.27783},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27783},
}
RIS
TY - UNPB
TI - Size and spectral radius conditions for the existence of k-factor in graphs with given minimum degree
AU - Zengzhao Xu
AU - Bo Deng
AU - Ligong Wang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27783
UR - https://arxiv.org/abs/2610.27783
AB - In recent years, characterizing the conditions for the existence of an [a,b]-factor in graphs has received significant academic attention. For integers b≥ a≥ 1, an $[a, b]$-factor of a graph G is defined as a spanning subgraph H such that a≤ d_H(v)≤ b for every v∈ V(G). If a=b=k, a $[k, k]$-factor is called a k-factor of G. Let δ(G) denote the minimum degree of a graph G. Hao and Li [Electron. J. Combin. (2024)] posed the problem of characterizing the size or spectral radius conditions for a graph to contain an [a,b]-factor with δ(G)≥ a. Fan, Lin and Zhu [Discrete Math. (2026)] solved the size version of this problem for the case a < b. In this paper, for a=b=k, we characterize the size condition for a graph to have a k-factor with δ(G)≥ k. Using this result, we also characterize the spectral radius and distance spectral radius conditions for a graph to have a k-factor, respectively.
ER -