Graphs with few 3-cliques and 3-anticliques are 3-universal

2013/06/09 by Nati Linial, Linial, Nati, Avraham Morgenstern +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Ask price #Combinatorics #Combinatorics (math.CO) #Discrete mathematics #FOS: Mathematics #Graph #Limits and Structures in Graph Theory #Mathematics #Phenomenon #Physics #Quantum mechanics #Vertex (graph theory) #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1306.2020

12 pages, 1 figure

openalex publication_date 2013/06/09 · arxiv created 2014/02/18 · arxiv updated 2014/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

For given integers k, l we ask whether every large graph with a sufficiently small number of k-cliques and k-anticliques must contain an induced copy of every l-vertex graph. Here we prove this claim for k=l=3 with a sharp bound. A similar phenomenon is established as well for tournaments with k=l=4.

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