Spectral radius and size conditions for fractional (a,b,m)-covered graphs

2025/12/23 by Xu, Zengzhao, Wang, Ligong, Xi, Weige
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.20089

Abstract

A fractional (a,b,m)-covered graph is a generalization of the concept of a fractional [a,b]-covered graph. For any H ⊆ G with edge set |E(H)| = m, if there exists a fractional [a,b]-factor (the corresponding fractional indicator function is h) such that h(e) = 1 for any e ∈ H, then the graph G is called a fractional (a,b,m)-covered graph. In this paper, we characterize the conditions for a graph to be a fractional (a,b,m)-covered graph from the perspectives of spectral radius and size, respectively.

Citations

• Eigenvalues and factors: a survey
• Spectral radius, fractional [a,b]-factor and ID-factor-critical graphs
• Fractional matching, factors and spectral radius in graphs involving minimum degree
• Spectral radius conditions for fractional [a,b]-covered graphs

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