The maximum k-colorable subgraph problem
The main topic of this Masters thesis is the study of the maximum k-colorable subgraph problem using techniques from polyhedral theory, convex relaxations and semidefinite programming. Given a graph, one wants to find a largest induced subgraph whose vertices can be colored with k colors. In the cas...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Brasil |
| Institución: | Universidade de São Paulo (USP) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da USP |
| Idioma: | inglés |
| OAI Identifier: | oai:teses.usp.br:tde-25082025-111037 |
| Acceso en línea: | https://www.teses.usp.br/teses/disponiveis/45/45134/tde-25082025-111037/ |
| Access Level: | acceso abierto |
| Palabra clave: | Conjuntos estáveis Função theta de Lovász Lovászs theta function Programação semidefinida Semidefinite programming Stable sets |
| Sumario: | The main topic of this Masters thesis is the study of the maximum k-colorable subgraph problem using techniques from polyhedral theory, convex relaxations and semidefinite programming. Given a graph, one wants to find a largest induced subgraph whose vertices can be colored with k colors. In the case k = 1 the problem becomes the classical maximum stable set problem. Narasimhan introduced a polynomially computable bound for this problem which generalizes the Lovász theta function. In this dissertation we review basic results about the maximum stable set problem and its semidefinite relaxation, exhibit the bound introduced by Narasimhan, and develop novel connections based on the work of Lovász. |
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