Paper Info
Title
Large cliques or stable sets in graphs with no four-edge path and no five-edge path in the complement
Abstract
Erdős and Hajnal [Discrete Math 25 (1989), 37–52] conjectured that, for any graph H, every graph on n vertices that does not have H as an induced subgraph contains a clique or a stable set of size nɛ(H) for some ɛ(H)0. The Conjecture 1. known to be true for graphs H with |V(H)|≤4. One of the two remaining open cases on five vertices is the case where H is a four-edge path, the other case being a cycle of length five. In this article we prove that every graph on n vertices that does not contain a four-edge path or the complement of a five-edge path as an induced subgraph contains either a clique or a stable set of size at least n1/6. © 2011 Wiley Periodicals, Inc. J Graph Theory (This research was performed while the author was at Columbia University. © 2012 Wiley Periodicals, Inc.)
Year
DOI
Venue
2012
10.1002/jgt.20626
Journal of Graph Theory
Keywords
Field
DocType
induced subgraph,four-edge path,five-edge path,n vertex,graphs h,wiley periodicals,large clique,inc. j graph theory,graph h,size n,stable set
Discrete mathematics,Block graph,Combinatorics,Induced path,Induced subgraph,Independent set,Erdős–Hajnal conjecture,Clique (graph theory),Mathematics,Complement graph,Path graph
Journal
Volume
Issue
ISSN
70
4
0364-9024
Citations 
PageRank 
References 
7
0.73
3
Authors
2
Name
Order
Citations
PageRank
Maria Chudnovsky139046.13
Yori Zwols2456.34