Abstract
We consider maximum properly edge-colored trees in edge-colored graphs. We also consider the problem where, given a vertex r, determine whether the graph has a spanning tree rooted at r, such that all root-to-leaf paths are properly colored. We consider these problems from graph-theoretic as well as algorithmic viewpoints. We prove their optimization versions to be NP-hard in general and provide algorithms for graphs without properly edge-colored cycles. We also derive some nonapproximability bounds. A study of the trends random graphs display with regard to the presence of properly edge-colored spanning trees is presented.
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