文献类型：期刊文献

英文题名：Spectral extrema of Ks,t-Minor free graphs-On a conjecture of M. Tait

作者：Zhai, Mingqing[1]; Lin, Huiqiu[2]

机构：[1] School of Mathematics and Finance, Chuzhou University, Anhui, Chuzhou, 239012, China; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2021

外文期刊名：arXiv

收录：EI(收录号：20210259509)

语种：英文

外文关键词：Graph theory - Graphic methods

摘要：Minors play an important role in extremal graph theory and spectral extremal graph theory. Tait [The Colin de Verdière parameter, excluded minors, and the spectral radius, J. Combin. Theory Ser. A 166 (2019) 42-58] determined the maximum spectral radius and characterized the unique extremal graph for Kr-minor free graphs of sufficiently large order n, he also made great progress on Ks,t-minor free graphs and posed a conjecture: Let 2 ≤ s ≤ t and n ? s + 1 = pt + q, where n is sufficiently large and 1 ≤ q ≤ t. Then Ks?1?(pKt ∪Kq) is the unique extremal graph with the maximum spectral radius over all n-vertex Ks,t-minor free graphs. In this paper, Tait's conjecture is completely solved. We also determine the maximum spectral radius and its extremal graphs for n-vertex K1,tminor free graphs. To prove our results, some spectral and structural tools, such as, local edge maximality, local degree sequence majorization, double eigenvectors transformation, are used to deduce structural properties of extremal graphs. ? 2021, CC BY.