Affiliation:
1. Programa de Engenharia de Sistemas e Computação, COPPE Universidade Federal do Rio de Janeiro Rio de Janeiro Brazil
2. Instituto de Matemática e Estatística Universidade de São Paulo São Paulo Brazil
Abstract
AbstractThe mod chromatic index of a graph is the minimum number of colors needed to color the edges of in a way that the subgraph spanned by the edges of each color has all degrees congruent to . Recently, the authors proved that the mod chromatic index of every graph is at most , improving, for large , a result of Scott. Here we study the mod chromatic index of random graphs. We prove that for every integer , there is such that if and as , then the following holds: if is odd, then the mod chromatic index of is asymptotically almost surely (a.a.s.) equal to , while if is even, then the mod chromatic index of (respectively, ) is a.a.s. equal to (respectively, ).
Funder
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Subject
Geometry and Topology,Discrete Mathematics and Combinatorics