Work

Making K r +1 -free graphs r -partite

Year: 2020

Type: article

Abstract: The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a K r+ 1 -free graph on n vertices with e ( G ) > ex( n , K r +1 )– α n 2 , then one can remove εn 2 edges from G to obtain an r -partite graph. Füredi gave a short proof that one can choose α = ε . We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.

Source: Combinatorics Probability Computing

DOI: 10.1017/s0963548320000590

Authors: József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender

Institutions: Moscow Institute of Physics and Technology, University of Illinois Urbana-Champaign, Iowa State University, University of Colorado Denver

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,160

Funders: National Science Foundation, University of Illinois at Urbana-Champaign