Spectral Turán problems for intersecting even cycles

2023/03/27 by Dheer Noal Desai, Desai, Dheer Noal · 1 citation
Mathematics · #05C35 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2303.15635

openalex publication_date 2023/03/27 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28

Abstract

Let C_{2k1, 2k2, …, 2kt} denote the graph obtained by intersecting t distinct even cycles C_2k1, C_2k2, …, C_2kt at a unique vertex. In this paper, we determine the unique graphs with maximum adjacency spectral radius among all graphs on n vertices that do not contain any C_{2k1, 2k2, …, 2kt} as a subgraph, for n sufficiently large. When one of the constituent even cycles is a C₄, our results improve upper bounds on the Turán numbers for intersecting even cycles that follow from more general results of Füredi [20] and Alon, Krivelevich and Sudakov [1]. Our results may be seen as extensions of previous results for spectral Turán problems on forbidden even cycles C_2k, k≥ 2 (see [8, 34, 44, 45]).

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