Coloração de Arestas em Grafos Split-Comparabilidade

• Autor(a) principal: Cruz, Jadder Bismarck de Sousa
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/9140
• topic: Teoria dos grafos; Coloração de arestas; Problema da Classificação; Grafos comparabilidade; Classification Problem; Graph theory; Grafos split; Edge coloring; Chromatic index; Split graphs; Comparability graphs; CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

Let G = (V, E) be a simple and undirected graph. An edge-coloring is an assignment of colors to the edges of the graph such that any two adjacent edges receive different colors. The chromatic index of a graph G is the smallest number of colors such that G has an edge-coloring. Clearly, a lower bound for the chromatic index is the degree of the vertex of higher degree, denoted by ?(G). In 1964, Vizing proved that chromatic index is ?(G) or ?(G) + 1. The Classification Problem is to determine if the chromatic index is ?(G) (Class 1 ) or if it is ?(G) + 1 (Class 2 ). Let n be number of vertices of a graph G and let m be its number of edges. We say G is overfull if m > (n-1) 2 ?(G). Every overfull graph is Class 2. A graph is subgraph-overfull if it has a subgraph with same maximum degree and it is overfull. It is well-known that every overfull and subgraph-overfull graph is Class 2. The Overfull Conjecture asserts that every graph with ?(G) > n 3 is Class 2 if and only if it is subgraph-overfull. In this work we prove the Overfull Conjecture to a particular class of graphs, known as split-comparability graphs. The Overfull Conjecture was open to this class.