Spectral radius, fractional [a,b]-factor and ID-factor-critical graphs

• Published in: Discrete mathematics 2024-07, Vol.347 (7), p.113976, Article 113976
• Main Authors: Fan, Ao, Liu, Ruifang, Ao, Guoyan
• Format: Article
• Language: English
• Subjects: Fractional [formula omitted]-factor; ID-factor-critical; Minimum degree; Spectral radius
• ISSN: 0012-365X; 1872-681X
• DOI: 10.1016/j.disc.2024.113976

Let G be a graph and h:E(G)→[0,1] be a function. For any two positive integers a and b with a≤b, a fractional [a,b]-factor of G with the indicator function h is a spanning subgraph with vertex set V(G) and edge set Eh such that a≤∑e∈EG(v)h(e)≤b for any vertex v∈V(G), where Eh={e∈E(G)|h(e)>0} and EG(v)={e∈E(G)|eis incident withvinG}. A graph G is ID-factor-critical if for every independent set I of G whose size has the same parity as |V(G)|, G−I has a perfect matching. In this paper, we present a tight sufficient condition based on the spectral radius for a graph to contain a fractional [a,b]-factor, which extends the result of Wei and Zhang (2023) [16]. Furthermore, we also prove a tight sufficient condition in terms of the spectral radius for a graph with minimum degree δ to be ID-factor-critical.