TY - JOUR
T1 - Generalized rainbow Turán problems
AU - Gerbner, Dániel
AU - Mészáros, Tamás
AU - Methuku, Abhishek
AU - Palmer, Cory
N1 - ∗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.
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.
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.
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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 -