Sufficient conditions for even factors in graphs

2025/10/12 by Zhou, Sizhong, Bian, Qiuxiang, Wu, Jiancheng · 3 citations
#05C50 #05C70 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.10500

Abstract

Let G be a graph. We denote by e(G) and ρ(G) the size and the spectral radius of G. A spanning subgraph F of G is called an even factor of G if d_F(v)∈\2,4,6,…\ for every v∈ V(G). Yan and Kano provided a sufficient condition using the number of odd components in G-S for a graph G of even order to contain an even factor, where S is a vertex subset of G [Z. Yan, M. Kano, Strong Tutte type conditions and factors of graphs, Discuss. Math. Graph Theory 40 (2020) 1057--1065]. In this paper, motivated by Yan and Kano's above result, we present some tight sufficient conditions to guarantee that a connected graph G with the minimum degree δ contains an even factor with respect to its size and spectral radius.

Citations

• Some results on the k-strong parity property in a graph
• Sufficient conditions for a graph with minimum degree to have a component factor
• A spectral condition for spanning trees with restricted degrees in bipartite graphs
• Toughness and spectral radius in graphs
• Matching extension and matching exclusion via the size or the spectral radius of graphs
• Signless Laplacian spectral radius for a k-extendable graph
• Spectral conditions for graphs having all (fractional) [a,b]-factors
• Spectral radius and [a,b]-factors in graphs

Cited by

• The existence of even factors based on the A_α-spectral radius of graphs
• Signless Laplacian spectral conditions for even factors in graphs
• The existence of even factors based on spectral conditions of graphs

Related

• The existence of even factors based on spectral conditions of graphs
• The existence of even factors based on the A_α-spectral radius of graphs
• Signless Laplacian spectral conditions for even factors in graphs
• Sharp conditions for the existence of an even [a,b]-factor in a graph
• Spectral radius and [a,b]-factors in graphs