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On hypergraph Turán problems with bounded matching number

Dániel Gerbner, Casey Tompkins, Junpeng Zhou

Abstract

Very recently, Alon and Frankl, and Gerbner studied the maximum number of edges in $n$-vertex $F$-free graphs with bounded matching number, respectively. We consider the analogous Turán problems on hypergraphs with bounded matching number, and we obtain some exact results.

On hypergraph Turán problems with bounded matching number

Abstract

Very recently, Alon and Frankl, and Gerbner studied the maximum number of edges in -vertex -free graphs with bounded matching number, respectively. We consider the analogous Turán problems on hypergraphs with bounded matching number, and we obtain some exact results.

Paper Structure

This paper contains 6 sections, 16 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['thmnew1']}
  3. 2-chromatic case
  4. General hypergraphs
  5. Expansion of graphs with bounded matching number
  6. Concluding remarks

Key Result

Theorem 1.1

(gerbner) If $\chi(F)>2$ and $n$ is sufficiently large, then $\mathrm{ex}(n,\{F,M_{s+1}\})=\mathrm{ex}(s,{\mathcal{F}})+s(n-s)$, where ${\mathcal{F}}$ is the family of graphs obtained by deleting an independent set from $F$.

Theorems & Definitions (29)

  • Theorem 1.1
  • Proposition 1.2
  • Theorem 1.3: Fr1
  • Theorem 1.4
  • Proposition 1.5
  • Proposition 1.6
  • Theorem 1.7
  • Proposition 1.8
  • Theorem 1.9
  • Theorem \ref{thmnew1}
  • ...and 19 more