On the complexity of path problems in properly colored directed graphs
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Abstract
We address the complexity class of several problems related to finding a path in a properly colored directed graph. A properly colored graph is defined as a graph G whose vertex set is partitioned into \(\mathcal{X}(G)\) stable subsets, where \(\mathcal{X}(G)\) denotes the chromatic number of G. We show that to find a simple path that meets all the colors in a properly colored directed graph is NP-complete, and so are the problems of finding a shortest and longest of such paths between two specific nodes.
Keywords
Graph coloring Complexity Chromatic number Longest path Shortest pathPreview
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