2021/03/22 by Carlos Hoppen, Hoppen, Carlos, Hanno Lefmann +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.2103.11892
arxiv created 2021/03/22 · openalex publication_date 2021/03/22 · arxiv updated 2021/03/23 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
Given integers r ≥ 2, k ≥ 3 and 2 ≤ s ≤ \binomk2, and a graph G, we consider r-edge-colorings of G with no copy of a complete graph Kk on k vertices where s or more colors appear, which are called Pk,s-free r-colorings. We show that, for large n and r ≥ r0(k,s), the (k-1)-partite Turán graph Tk-1(n) on n vertices yields the largest number of Pk,s-free r-colorings among all n-vertex graphs, and that it is the unique graph with this property.