TY - JOUR

T1 - Some exact results for generalized Turán problems

AU - Gerbner, Dániel

AU - Palmer, Cory

N1 - Funding Information:
Research supported by the János Bolyai Research Fellowship of the Hungarian Academy of Sciences and the National Research, Development and Innovation Office – NKFIH, Hungary under the grants FK 132060, KKP-133819, KH130371 and SNN 129364.Research supported by a grant from the Simons Foundation #712036.
Publisher Copyright:
© 2022 Elsevier Ltd

PY - 2022/6

Y1 - 2022/6

N2 - Fix a k-chromatic graph F. In this paper we consider the question to determine for which graphs H does the Turán graph Tk−1(n) have the maximum number of copies of H among all n-vertex F-free graphs (for n large enough). We say that such a graph H is F-Turán-good. In addition to some general results, we give (among others) the following concrete results: (i) For every complete multipartite graph H, there is k large enough such that H is Kk-Turán-good. (ii) The path P3 is F-Turán-good for F with χ(F)≥4. (iii) The path P4 and cycle C4 are C5-Turán-good. (iv) The cycle C4 is F2-Turán-good where F2 is the graph of two triangles sharing exactly one vertex.

AB - Fix a k-chromatic graph F. In this paper we consider the question to determine for which graphs H does the Turán graph Tk−1(n) have the maximum number of copies of H among all n-vertex F-free graphs (for n large enough). We say that such a graph H is F-Turán-good. In addition to some general results, we give (among others) the following concrete results: (i) For every complete multipartite graph H, there is k large enough such that H is Kk-Turán-good. (ii) The path P3 is F-Turán-good for F with χ(F)≥4. (iii) The path P4 and cycle C4 are C5-Turán-good. (iv) The cycle C4 is F2-Turán-good where F2 is the graph of two triangles sharing exactly one vertex.

UR - http://www.scopus.com/inward/record.url?scp=85125116220&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2022.103519

DO - 10.1016/j.ejc.2022.103519

M3 - Article

AN - SCOPUS:85125116220

SN - 0195-6698

VL - 103

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

M1 - 103519

ER -