Induced Tur\'an problems and traces of hypergraphs
Zoltan Furedi, Ruth Luo

TL;DR
This paper explores the relationship between induced Berge subgraphs in hypergraphs and classical Turán problems, establishing connections between hypergraph edge extremal functions and graph clique counts.
Contribution
It introduces a new framework linking induced Berge hypergraph problems with traditional Turán graph extremal functions, providing new insights into hypergraph trace problems.
Findings
Established a strong relation between hypergraph extremal functions and graph clique counts.
Derived bounds connecting induced Berge hypergraph problems with classical Turán problems.
Provided new methods for analyzing hypergraph traces in the context of extremal combinatorics.
Abstract
Let be a graph. We say that a hypergraph contains an induced Berge if the vertices of can be embedded to (e.g., ) and there exists an injective mapping from the edges of to the hyperedges of such that holds for each edge of . In other words, contains as a trace. Let denote the maximum number of edges in an -uniform hypergraph with no induced Berge . Let denote the maximum number of 's in an -free graph on vertices. We show that these two Tur\'an type functions are strongly related.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph theory and applications
