Maximum number of r-edge-colorings such that all copies of Kk are rainbow

• Autor(a) principal: Bastos, Antônio Josefran de Oliveira
• Data de Publicação: 2021
• Outros Autores: Lefmann, Hanno, Oertel, Andy, Hoppen, Carlos, Schmidt, Dionatan Ricardo
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRGS
• Texto Completo: http://hdl.handle.net/10183/246900
• topic: Grafos; Coloração de arestas; Arco-iris; Edge-colorings; Turán problem; Erdős-Rothschild problem

We consider a version of the Erdős-Rothschild problem for families of graph patterns. For any fixed k ≥ 3, let r0(k) be the largest integer such that the following holds for all 2 ≤ r ≤ r0(k) and all sufficiently large n: The Turán graph Tk-1(n) is the unique n-vertex graph G with the maximum number of r-edge-colorings such that the edge set of any copy of Kk in G is rainbow. We use the regularity lemma of Szemerédi and linear programming to obtain a lower bound on the value of r0(k). For a more general family P of patterns of Kk, we also prove that, in order to show that the Turán graph Tk-1(n) maximizes the number of P-free r-edge-colorings over n-vertex graphs, it suffices to prove a related stability result.