TY - JOUR

T1 - Supersaturation Problem for the Bowtie

AU - Kang, Mihyun

AU - Makai, Tamas

AU - Pikhurko, Oleg

PY - 2017

Y1 - 2017

N2 - The Turán function ex(n, F) denotes the maximal number of edges in an F-free graph on n vertices. However if e>ex(n,F), many copies of F appear. We study the function hF(n, q), the minimal number of copies of F in a graph on n vertices with ex(n, F) + q edges. The value of hF(n, q) has been extensively studied when F is colour critical. In this paper we consider a simple non-colour-critical graph, namely the bowtie and establish bounds on hF (n, q) for different ranges of q.

AB - The Turán function ex(n, F) denotes the maximal number of edges in an F-free graph on n vertices. However if e>ex(n,F), many copies of F appear. We study the function hF(n, q), the minimal number of copies of F in a graph on n vertices with ex(n, F) + q edges. The value of hF(n, q) has been extensively studied when F is colour critical. In this paper we consider a simple non-colour-critical graph, namely the bowtie and establish bounds on hF (n, q) for different ranges of q.

U2 - 10.1016/j.endm.2017.07.023

DO - 10.1016/j.endm.2017.07.023

M3 - Conference article

SN - 1571-0653

VL - 61

SP - 679

EP - 685

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -