2022/03/25 by Vic Bednar, Bednar, Vic, Neal Bushaw +1 · 1 citation
Computer Science · Mathematics · #05DXX #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2203.13765
openalex publication_date 2022/03/25 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
The rainbow Turán number, a natural extension of the well studied traditional Turán number, was introduced in 2007 by Keevash, Mubayi, Sudakov and Verstraëte. The rainbow Turán number of a graph H, ex*(n,H), is the largest number of edges for an n vertex graph G which can be properly edge colored with no rainbow H subgraph. We explore the reduction method for finding upper bounds on rainbow Turán numbers, and use this to inform results for the rainbow Turán numbers of double stars, caterpillars, and perfect binary trees. In addition, we define k-unique colorings and the related k-unique Turán numbers. We provide preliminary results on this new variant on the classic problem.