Author:
Long Eoin,Ploscaru Laurenţiu
Abstract
AbstractAn old conjecture of Erdős and McKay states that if all homogeneous sets in an
$n$
-vertex graph are of order
$O(\!\log n)$
then the graph contains induced subgraphs of each size from
$\{0,1,\ldots, \Omega \big(n^2\big)\}$
. We prove a bipartite analogue of the conjecture: if all balanced homogeneous sets in an
$n \times n$
bipartite graph are of order
$O(\!\log n)$
, then the graph contains induced subgraphs of each size from
$\{0,1,\ldots, \Omega \big(n^2\big)\}$
.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference34 articles.
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