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October 16, 2025Open Access

Generalized Turán results for disjoint copies of degenerate graphs

Key Points

The study establishes precise bounds for generalized Turán numbers using forbidden graphs.
It focuses on disjoint copies of structures like (t+1)K_{a,b} and (t+1)C_{2k}.
Research builds on previous work by Gerbner, Methuku, and Vizer, providing sharp asymptotic results.
Findings may aid in understanding extremal graph theory and graph configurations.

Abstract

The generalized Turán number ex (n, H, F) denotes the maximum number of copies of H in an n-vertex F-free graph. For an integer t 1, let tF be the vertex-disjoint union of t copies of F. Gerbner, Methuku, and Vizer (2019) established an asymptotically sharp bound for ex (n, Kᵣ, (t+1) K₂, ₁). We extend their results in two directions by considering forbidden graphs (t+1) K₀, ₁ and (t+1) C₂₊ and establish more precise matching upper and lower bounds of the same order of magnitude.

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Cite This Study

Yang et al. (Fri,) studied this question.

synapsesocial.com/papers/68f10ecee6a12fd042899a53 https://doi.org/https://doi.org/10.48550/arxiv.2508.06043

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