English

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

Combinatorics 2025-12-24 v1

Abstract

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

Keywords

Cite

@article{arxiv.2512.20089,
  title  = {Spectral radius and size conditions for fractional $(a,b,m)$-covered graphs},
  author = {Zengzhao Xu and Ligong Wang and Weige Xi},
  journal= {arXiv preprint arXiv:2512.20089},
  year   = {2025}
}