Title: On maximal dominating forest and four colors theorem of planar graph
Abstract: For a given graph $G(V,E)$ and one of its dominating set $S$, the subgraph $G\left[S\right]$ induced by $S$ is a called a dominating tree if $G\left[S\right]$ is a tree. Not all graphs has a dominating tree, we will show that a graph without cut vertices has at least one dominating tree. Analogously, if $G\left[S\right]$ is a forest, then it is called a dominating forest. As special structures of graphs, dominating tree and dominating forest have many interesting application, and we will focus on its application on the problem of planar graph coloring.
Publication Year: 2021
Publication Date: 2021-09-05
Language: en
Type: preprint
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