TY - JOUR

T1 - Generalized rainbow Turán problems

AU - Gerbner, Dániel

AU - Mészáros, Tamás

AU - Methuku, Abhishek

AU - Palmer, Cory

N1 - Funding Information:
∗Supported by the János Bolyai Research Fellowship of the Hungarian Academy of Sciences and the National Research, Development and Innovation Office – NKFIH under the grants K 116769, KH130371 and SNN 129364. †Supported by the Dahlem Research School. ‡Supported by EPSRC grant EP/S00100X/1 (A. Methuku) and by IBS-R029-C1. §Supported by a grant from the Simons Foundation #712036.
Funding Information:
Supported by the János Bolyai Research Fellowship of the Hungarian Academy of Sciences and the National Research, Development and Innovation Office – NKFIH under the grants K 116769, KH130371 and SNN 129364. Supported by the Dahlem Research School. Supported by EPSRC grant EP/S00100X/1 (A. Methuku) and by IBS-R029-C1. Supported by a grant from the Simons Foundation #712036.
Publisher Copyright:
© The authors.

PY - 2022

Y1 - 2022

N2 - Alon and Shikhelman [J. Comb. Theory, B. 121 (2016)] initiated the systematic study of the following generalized Turán problem: for fixed graphs H and F and an integer n, what is the maximum number of copies of H in an n-vertex F-free graph? An edge-colored graph is called rainbow if all its edges have different colors. The rainbow Turán number of F is defined as the maximum number of edges in a properly edge-colored graph on n vertices with no rainbow copy of F . The study of rainbow Turán problems was initiated by Keevash, Mubayi, Sudakov and Verstraëte [Comb. Probab. Comput. 16 (2007)]. Motivated by the above problems, we study the following problem: What is the maximum number of copies of F in a properly edge-colored graph on n vertices without a rainbow copy of F? We establish several results, including when F is a path, cycle or tree.

AB - Alon and Shikhelman [J. Comb. Theory, B. 121 (2016)] initiated the systematic study of the following generalized Turán problem: for fixed graphs H and F and an integer n, what is the maximum number of copies of H in an n-vertex F-free graph? An edge-colored graph is called rainbow if all its edges have different colors. The rainbow Turán number of F is defined as the maximum number of edges in a properly edge-colored graph on n vertices with no rainbow copy of F . The study of rainbow Turán problems was initiated by Keevash, Mubayi, Sudakov and Verstraëte [Comb. Probab. Comput. 16 (2007)]. Motivated by the above problems, we study the following problem: What is the maximum number of copies of F in a properly edge-colored graph on n vertices without a rainbow copy of F? We establish several results, including when F is a path, cycle or tree.

UR - http://www.scopus.com/inward/record.url?scp=85133723437&partnerID=8YFLogxK

U2 - 10.37236/9964

DO - 10.37236/9964

M3 - Article

AN - SCOPUS:85133723437

SN - 1077-8926

VL - 29

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 2

M1 - #P2.44

ER -