# Journal article

## Pure pairs. V. Excluding some long subdivision

Abstract:

A pure pair in a graph $G$ is a pair $A,B$ of disjoint subsets of $V(G)$ such that $A$ is complete or anticomplete to $B$. Jacob Fox showed that for all $\epsilon>0$, there is a comparability graph $G$ with $n$ vertices, where $n$ is large, in which there is no pure pair $A,B$ with $|A|,|B|\ge \epsilon n$. He also proved that for all $c>0$ there exists $\epsilon>0$ such that for every comparability graph $G$ with $n>1$ vertices, there is a pure pair $A,B$ with \$|A|,|B|\ge \epsilon...

Publication status:
Accepted
Peer review status:
Peer reviewed

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author
ORCID:
0000-0003-4489-5988
Publisher:
Springer Nature Publisher's website
Journal:
Combinatorica Journal website
Acceptance date:
2023-01-24
EISSN:
1439-6912
ISSN:
0209-9683
Language:
English
Keywords:
Pubs id:
1176186
Local pid:
pubs:1176186
Deposit date:
2023-01-24