The sparse regularity method for graphs with few even-cycle homomorphisms

Nan Zhang

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arXiv · 2610.35421

The sparse regularity method for graphs with few even-cycle homomorphisms

Nan Zhang

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Abstract

Let $C_k$ denote a cycle on $k$ vertices. Pascadi (2026) established a removal lemma for $C_{2k+1}$ in graphs with few $C_{2k}$-homomorphisms under a dense-pairs condition, using Schatten--von Neumann norms and entropy methods. We give a short proof of a version with more restrictive partition and diagonal requirements, extending the combinatorial approach of Conlon, Fox, Sudakov and Zhao (2021) without using Pascadi's Schatten-norm regularity framework. We illustrate the method with a known sparse removal statement for odd product equations in finite groups.

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Nan Zhang. 2026-10-26. The sparse regularity method for graphs with few even-cycle homomorphisms. https://arxiv.org/abs/2610.35421

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