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The prevalence conjecture for regular partitions in real-world structures
A graph is a finite set of nodes together with edges between pairs of nodes. A regular partition is a partition of the node set into parts whose induced bipartite graphs are nearly…
Conjectureopengraph-theory network-science regularity-lemmaarXiv posted 2 days ago
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Kohayakawa–Łuczak–Rödl conjecture on triangles in sparse regular triples
Let $G$ be a graph, and let $(V_1,V_2,V_3)$ be a triple of pairwise disjoint vertex sets such that each pair $(V_i,V_j)$ is $(\varepsilon,p)$ -regular, meaning that for all…
Conjectureopenregularity-lemma sparse-graphs triangle-packingsarXiv posted 2 days ago

The prevalence conjecture for regular partitions in real-world structures