Conditions for k-factor-critical graphs
Year: 2025
Type: article
Abstract: For a nonnegative integer k, a graph G is said to be k-factor-critical if G − T has a perfect matching for any subset T ⊆ V (G) with |T | = k. In this paper, we first provide a condition in terms of the size of G to guarantee that G is k-factor-critical. For any graph G with minimum degree δ, we deduce a lower bound on the signless Laplacian spectral radius of G to ensure that G is k-factor-critical. Furthermore, we establish a condition based on Laplacian eigenvalues (resp. toughness) to determine whether a graph G is k-factor-critical. Additionally, we introduce a nullity condition for a t-connected graph to be k-factor-critical.
Source: RAIRO - Operations Research
DOI: 10.1051/ro/2025093
Authors: Xiaoyun Lv, Hongzhang Chen, Jianxi Li, Shou-Jun Xu
Institutions: Lanzhou University, Minnan Normal University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412030652