Abstract: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.
| Subjects: | Combinatorics (math.CO) |
| Cite as: | arXiv:2605.24940 [math.CO] |
| (or arXiv:2605.24940v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24940 arXiv-issued DOI via DataCite (pending registration) |
From: Béla Csaba [view email]
[v1]
Sun, 24 May 2026 08:38:51 UTC (22 KB)
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