Author:
Gishboliner Lior,Sudakov Benny
Abstract
AbstractA chordal graph is a graph with no induced cycles of length at least
$4$
. Let
$f(n,m)$
be the maximal integer such that every graph with
$n$
vertices and
$m$
edges has a chordal subgraph with at least
$f(n,m)$
edges. In 1985 Erdős and Laskar posed the problem of estimating
$f(n,m)$
. In the late 1980s, Erdős, Gyárfás, Ordman and Zalcstein determined the value of
$f(n,n^2/4+1)$
and made a conjecture on the value of
$f(n,n^2/3+1)$
. In this paper we prove this conjecture and answer the question of Erdős and Laskar, determining
$f(n,m)$
asymptotically for all
$m$
and exactly for
$m \leq n^2/3+1$
.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
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