Decomposition of degree-regular graphs into quasi-random pairs without the Regularity lemma

Fuente: arXiv
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Autore principale: Csaba, Béla
Natura: Preprint
Pubblicazione: 2026
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author Csaba, Béla
author_facet Csaba, Béla
contents The Szemerédi Regularity Lemma, in combination with the Blow-up Lemma, form the Regularity Method, a fundamental tool in graph embeddings, albeit restricted to very large and dense graphs. We propose an alternative vertex-partitioning framework that remains effective even as the density tends to zero and without requiring astronomically large vertex sets. This approach, while narrower in scope, extends regularity-type techniques to relatively small graphs previously inaccessible to the Regularity Method. As an application, we use this novel vertex-partitioning method for bipartite packing problems.
format Preprint
id arxiv_https___arxiv_org_abs_2605_24940
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Decomposition of degree-regular graphs into quasi-random pairs without the Regularity lemma
Csaba, Béla
Combinatorics
The Szemerédi Regularity Lemma, in combination with the Blow-up Lemma, form the Regularity Method, a fundamental tool in graph embeddings, albeit restricted to very large and dense graphs. We propose an alternative vertex-partitioning framework that remains effective even as the density tends to zero and without requiring astronomically large vertex sets. This approach, while narrower in scope, extends regularity-type techniques to relatively small graphs previously inaccessible to the Regularity Method. As an application, we use this novel vertex-partitioning method for bipartite packing problems.
title Decomposition of degree-regular graphs into quasi-random pairs without the Regularity lemma
topic Combinatorics
url https://arxiv.org/abs/2605.24940