Algorithms for Finding Generalized Coloring of Trees
Let � be a positive integer, and � be a graph with nonnegative integer weights on edges. Then a generalized vertex-coloring, called an �-vertex-coloring of �, is an assignment of colors to the vertices in such a way that any two vertices � and � get different colors if the distance between � and � i...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Brasil |
| Institución: | Universidade Federal de Lavras (UFLA) |
| Repositorio: | INFOCOMP: Jornal de Ciência da Computação |
| Idioma: | inglés |
| OAI Identifier: | oai:infocomp.dcc.ufla.br:article/326 |
| Acceso en línea: | https://infocomp.dcc.ufla.br/index.php/infocomp/article/view/326 |
| Access Level: | acceso abierto |
| Palabra clave: | Algorithm Chordal Gra ph l-chromatic-number l-edge-coloring l-vertex-coloring Graph Tree |
| Sumario: | Let � be a positive integer, and � be a graph with nonnegative integer weights on edges. Then a generalized vertex-coloring, called an �-vertex-coloring of �, is an assignment of colors to the vertices in such a way that any two vertices � and � get different colors if the distance between � and � in � is at most �. A coloring is optimal if it usesminimumnumber of distinct colors. The �-vertex-coloring problem is to find an optimal �-vertex-coloring of a graph �. In this paper we present an ���� � ������ time algorithm to find an �-vertex-coloring of a tree � , where � is the maximum degree of � . The algorithm takes ����� time if both � and � are bounded integers. We compute the upper bound of colors to be � � ������������� ����� . We also present an ���� � ������ time algorithm for solving the �-edge-coloring problem of trees. If both � and � are bounded integers, this algorithm also takes ����� time. |
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