Coloração de arestas em grafos split com grau máximo par
A proper edge coloring of a graph is an assignment of colors to the edges of such that adjacent edges have distinct colors. The chromatic index of a graph , denoted ′(), is the minimum number of colors for which has a proper edge coloring. Since every pair of adjacent edges must have distinct colors...
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| Formato: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Recursos: | Universidade Tecnológica Federal do Paraná (UTFPR) |
| Repositorio: | Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT)) |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.utfpr.edu.br:1/31612 |
| Acesso em linha: | http://repositorio.utfpr.edu.br/jspui/handle/1/31612 |
| Access Level: | acceso abierto |
| Palavra-chave: | Algoritmos Otimização combinatória Teoria dos grafos Algorithms Combinatorial optimization Graph theory CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Engenharia/Tecnologia/Gestão |
| Resumo: | A proper edge coloring of a graph is an assignment of colors to the edges of such that adjacent edges have distinct colors. The chromatic index of a graph , denoted ′(), is the minimum number of colors for which has a proper edge coloring. Since every pair of adjacent edges must have distinct colors, ′() ≥ Δ(), where Δ() is the maximum degree of . In 1964, Vizing established that ′() ≤ Δ() + 1 for any simple graph . Graphs with ′() = Δ() are said to be Class 1, while graphs with ′() = Δ() + 1 are said to be Class 2. Despite the tight bounds for the chromatic index, determining ′() for an arbitrary graph is a difficult computational problem, known to be NP-complete. A graph is split if its vertex set can be partitioned into a clique and a stable set . In 2012, Almeida showed that to determine the chromatic index of split graphs it is sufficient to consider the cases where every vertex in has maximum degree. Considering this fact, in this master’s dissertation, we show that if the neighborhood of a subset , formed by the vertices of with degree at most Δ()/2, has at least ⌊||/2⌋ vertices, then is Class 1. In the remaining cases we characterize the subgraph-overfull split graphs. |
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