TY - JOUR

T1 - Unavoidable order-size pairs in hypergraphs — positive forcing density

AU - Axenovich, Maria

AU - Balogh, József

AU - Clemen, Felix Christian

AU - Weber, Lea

N1 - Publisher Copyright:
© The authors.

PY - 2023

Y1 - 2023

N2 - Erdős, Füredi, Rothschild and Sós initiated a study of classes of graphs that forbid every induced subgraph on a given number m of vertices and number f of edges. Extending their notation to r-graphs, we write (n, e) →r (m, f) if every r-graph G on n vertices with e edges has an induced subgraph on m vertices and f edges. The forcing density of a pair (m, f) is (Formula presented). In the graph setting it is known that there are infinitely many pairs (m, f) with positive forcing density. Weber asked if there is a pair of positive forcing density for r ≥ 3 apart from the trivial ones (m, 0) and (m, (mr)). Answering her question, we show that (6, 10) is such a pair for r = 3 and conjecture that it is the unique such pair. Further, we find necessary conditions for a pair to have positive forcing density, supporting this conjecture.

AB - Erdős, Füredi, Rothschild and Sós initiated a study of classes of graphs that forbid every induced subgraph on a given number m of vertices and number f of edges. Extending their notation to r-graphs, we write (n, e) →r (m, f) if every r-graph G on n vertices with e edges has an induced subgraph on m vertices and f edges. The forcing density of a pair (m, f) is (Formula presented). In the graph setting it is known that there are infinitely many pairs (m, f) with positive forcing density. Weber asked if there is a pair of positive forcing density for r ≥ 3 apart from the trivial ones (m, 0) and (m, (mr)). Answering her question, we show that (6, 10) is such a pair for r = 3 and conjecture that it is the unique such pair. Further, we find necessary conditions for a pair to have positive forcing density, supporting this conjecture.

KW - Induced hypergraphs

KW - forcing density

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U2 - 10.5070/C63362798

DO - 10.5070/C63362798

M3 - Article

AN - SCOPUS:85180671091

SN - 2766-1334

VL - 3

JO - Combinatorial Theory

JF - Combinatorial Theory

IS - 3

M1 - 15

ER -