TY - JOUR
T1 - Supersaturation problem for the bowtie
AU - Kang, M.
AU - Makai, T.
AU - Pikhurko, O.
PY - 2020
Y1 - 2020
N2 - The Turán function ex(n,F) denotes the maximal number of edges in an F-free graph on n vertices. We consider the function h
F(n,q), the minimal number of copies of F in a graph on n vertices with ex(n,F)+q edges. The value of h
F(n,q) has been extensively studied when F is bipartite or colour-critical. In this paper we investigate the simplest remaining graph F, namely, two triangles sharing a vertex, and establish the asymptotic value of h
F(n,q) for q=o(n
2).
AB - The Turán function ex(n,F) denotes the maximal number of edges in an F-free graph on n vertices. We consider the function h
F(n,q), the minimal number of copies of F in a graph on n vertices with ex(n,F)+q edges. The value of h
F(n,q) has been extensively studied when F is bipartite or colour-critical. In this paper we investigate the simplest remaining graph F, namely, two triangles sharing a vertex, and establish the asymptotic value of h
F(n,q) for q=o(n
2).
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85082726534&partnerID=MN8TOARS
U2 - 10.1016/j.ejc.2020.103107
DO - 10.1016/j.ejc.2020.103107
M3 - Article
SN - 1095-9971
VL - 88
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103107
ER -