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 -