文献类型：期刊文献

英文题名：Spectral conditions for forbidden subgraphs in bipartite graphs

作者：Ren, Yuan[1]; Zhang, Jing[1]; Zhang, Zhiyuan[1]

机构：[1] School of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2023

外文期刊名：arXiv

收录：EI(收录号：20230049987)

语种：英文

外文关键词：Matrix algebra - Trees (mathematics)

摘要：A graph G is H-free, if it contains no H as a subgraph. A graph is said to be H-minor free, if it does not contain H as a minor. In recent years, Nikiforov asked that what is the maximum spectral radius of an H-free graph of order n? In this paper, we consider about some Brualdi-Solheid-Turán type problems on bipartite graphs. In 2015, Zhai, Lin and Gong proved that if G is a bipartite graph with order n ≥ 2k + 2 and ρ(G) ≥ ρ(Kk,n?k), then G contains a C2k+2 unless G ～= Kk,n?k [Linear Algebra Appl. 471 (2015)]. Firstly, we give a new and more simple proof for the above theorem. Secondly, we prove that if G is a bipartite graph with order n ≥ 2k + 2 and ρ(G) ≥ ρ(Kk,n?k), then G contains all T2k+3 unless G ～= Kk,n?k. Finally, we prove that among all outerplanar bipartite graphs on n > 344569 vertices, K1,n?1 attains the maximum spectral radius. ? 2023, CC BY-NC-ND.