Generalized rainbow Turan problems

Gerbner, Dániel and Mészáros, Tamás and Methuku, Abhishek and Palmer, Cory (2022) Generalized rainbow Turan problems. ELECTRONIC JOURNAL OF COMBINATORICS, 29 (2). ArtNo: P2.44. ISSN 1077-8926

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Abstract

Alon and Shikhelman [J. Comb. Theory, B. 121 (2016)] initiated the systematic study of the following generalized Turan 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 Turan 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 Turan 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.

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