Geodesic
Generalized rainbow Turán problems
Dániel Gerbner1 ; Tamás Mészáros ; Abhishek Methuku2 ; Cory Palmer3
1Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
2Institute for Basic Science
3University of Montana
The electronic journal of combinatorics, Tome 29 (2022) no. 2
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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 Verstraete [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.
DOI : 10.37236/9964
Classification : 05C30, 05C15, 05C35
Mots-clés : rainbow Turán number, Erdős-Stone-Simonovits theorem

Dániel Gerbner  1   ; Tamás Mészáros    ; Abhishek Methuku  2   ; Cory Palmer  3

1 Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences
2 Institute for Basic Science
3 University of Montana 
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     title = {Generalized rainbow {Tur\'an} problems},
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Dániel Gerbner; Tamás Mészáros; Abhishek Methuku; Cory Palmer. Generalized rainbow Turán problems. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/9964

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