@article{Wang2026, 
author = {Xiangdong Wang and Zhenyu Ni},
title = {Research on spectral Turán problems under coexistence constraints of matching and color-critical graphs},
year = {2026},
journal = {Natural Science of Hainan University},
volume = {44},
number = {4},
pages = {451-457},
keywords = {chromatic critical graph, maximum spectral radius, Turán problem, extremal graph},
url = {https://www.sciopen.com/article/10.65658/j.hndk.2026010802},
doi = {10.65658/j.hndk.2026010802},
abstract = {This paper investigates the spectral Turán problem for graphs simultaneously excluding a matching  Ms+1 of size  s+1 and a color-critical graph  F with chromatic number  r+1. By introducing combinatorial parameters such as the covering number and independent covering number of the graph, this paper develops a unified framework for analyzing spectral extremal problems of degenerate forbidden graph families. Based on this framework, it is proved that, for sufficiently large  s, the maximum spectral radius of an  n-vertex  {Ms+1,F}-free graph is attained by the complete  r-partite graph  G(n,r,s), and this extremal graph is uniquely determined. This result not only extends the edge-extremal results of Alon and Frankl to the spectral setting, but also completely determines the spectral extremal structure under the coexistence constraints of matchings and color-critical graphs in this setting.}
}