TY - JOUR

T1 - Many disjoint triangles in co-triangle-free graphs

AU - Tyomkyn, Mykhaylo

N1 - Publisher Copyright:
© The Author(s), 2020. Published by Cambridge University Press.

PY - 2021/1

Y1 - 2021/1

N2 - We prove that any n-vertex graph whose complement is triangle-free contains n2/12 − o(n2) edge-disjoint triangles. This is tight for the disjoint union of two cliques of order n/2. We also prove a corresponding stability theorem, that all large graphs attaining the above bound are close to being bipartite. Our results answer a question of Alon and Linial, and make progress on a conjecture of Erdos.

AB - We prove that any n-vertex graph whose complement is triangle-free contains n2/12 − o(n2) edge-disjoint triangles. This is tight for the disjoint union of two cliques of order n/2. We also prove a corresponding stability theorem, that all large graphs attaining the above bound are close to being bipartite. Our results answer a question of Alon and Linial, and make progress on a conjecture of Erdos.

UR - http://www.scopus.com/inward/record.url?scp=85094939472&partnerID=8YFLogxK

U2 - 10.1017/S096354832000036X

DO - 10.1017/S096354832000036X

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AN - SCOPUS:85094939472

SN - 0963-5483

VL - 30

SP - 153

EP - 162

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 1

ER -