Uniquely list colorability of the graph Kn2 + Om

• Autor: Xuan Hung, Le
• Formato: artículo
• Fecha de Publicación: 2020
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revista UNITRU - Selecciones Matemáticas
• Lenguaje: español; inglés
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/2953
• Enlace del recurso: http://revistas.unitru.edu.pe/index.php/SSMM/article/view/2953
• Nivel de acceso: acceso abierto
• Materia: Vertex coloring (coloring); list coloring; uniquely list colorable graph; complete r-partite graph

Given a list L(v) for each vertex v, we say that the graph G is L-colorable if there is a proper vertex coloring of G where each vertex v takes its color from L(v). The graph is uniquely k-list colorable if there is a list assignment L such that jL(v)j = k for every vertex v and the graph has exactly one L-coloring with these lists. In this paper, we characterize uniquely list colorability of the graph G = Kn2 + Om. We shall prove that if n = 2 then G is uniquely 3-list colorable if and only if m >= 9, if n = 3 and m >=1 then G is uniquely 3-list colorable, if n >=4 then G is uniquely k-list colorable with k =[m/2]+1, and if m>=n-1, entonce G es UnLC.