Decomposition of degree-regular graphs into quasi-random pairs without the Regularity lemma
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917529078726656 |
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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 |