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arXiv · 2303.15635

Spectral Tur\'an problems for intersecting even cycles

Dheer Noal Desai
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Abstract

Let $C_{2k_1, 2k_2, \ldots, 2k_t}$ denote the graph obtained by intersecting $t$ distinct even cycles $C_{2k_1}, C_{2k_2}, \ldots, C_{2k_t}$ 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 $C_{2k_1, 2k_2, \ldots, 2k_t}$ as a subgraph, for $n$ sufficiently large. When one of the constituent even cycles is a $C_4$, our results improve upper bounds on the Tur\'an numbers for intersecting even cycles that follow from more general results of F\"{u}redi [20] and Alon, Krivelevich and Sudakov [1]. Our results may be seen as extensions of previous results for spectral Tur\'an problems on forbidden even cycles $C_{2k}, k\ge 2$ (see [8, 34, 44, 45]).

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Dheer Noal Desai. 2023-03-27. Spectral Tur\'an problems for intersecting even cycles. https://arxiv.org/abs/2303.15635

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