On the densities of cliques and independent sets in graphs

Hao Huang; Nati Linial; Humberto Naves; Yuval Peled; Benny Sudakov

doi:10.1007/s00493-015-3051-9

On the densities of cliques and independent sets in graphs

Hao Huang^*, Nati Linial, Humberto Naves, Yuval Peled, Benny Sudakov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Let r; s≥2 be integers. Suppose that the number of blue r-cliques in a red/blue coloring of the edges of the complete graph K_n is known and fixed. What is the largest possible number of red s-cliques under this assumption? The well known Kruskal-Katona theorem answers this question for r = 2 or s = 2. Using the shifting technique from extremal set theory together with some analytical arguments, we resolve this problem in general and prove that in the extremal coloring either the blue edges or the red edges form a clique.

Original language	English
Pages (from-to)	493-512
Number of pages	20
Journal	Combinatorica
Volume	36
Issue number	5
DOIs	https://doi.org/10.1007/s00493-015-3051-9
State	Published - 1 Oct 2016

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© 2016, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.

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abstract = "Let r; s≥2 be integers. Suppose that the number of blue r-cliques in a red/blue coloring of the edges of the complete graph Kn is known and fixed. What is the largest possible number of red s-cliques under this assumption? The well known Kruskal-Katona theorem answers this question for r = 2 or s = 2. Using the shifting technique from extremal set theory together with some analytical arguments, we resolve this problem in general and prove that in the extremal coloring either the blue edges or the red edges form a clique.",

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AU - Huang, Hao

AU - Linial, Nati

AU - Naves, Humberto

AU - Peled, Yuval

AU - Sudakov, Benny

PY - 2016/10/1

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On the densities of cliques and independent sets in graphs

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