Every Graph $G$ is Hall $\Delta(G)$-Extendible

[摘要] In the context of list coloring the vertices of a graph, Hall's condition is a generalization of Hall's Marriage Theorem and is necessary (but not sufficient) for a graph to admit a proper list coloring. The graph $G$ with list assignment $L$, abbreviated

[学科分类] 离散数学和组合数学

[关键词] Vertex coloring;List coloring;Precoloring Extension;Hall's condition;Hall $k$-extendible.