Connected Tropical Subgraphs in Vertex-Colored Graphs
نویسندگان
چکیده
A subgraph of a vertex-colored graph is said to be tropical whenever it contains each color of the graph. In this work we study the problem of finding a minimal connected tropical subgraph. We first show that this problem is NP-Hard for trees, interval graphs and split graphs, but polynomial when the number of colors is logarithmic in terms of the order of the graph (i.e. FPT). We then provide upper bounds for the order of the minimal connected tropical subgraph under various conditions. We finally study the problem of finding a connected tropical subgraph in a randomly vertex-colored random graph.
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عنوان ژورنال:
- Discrete Mathematics & Theoretical Computer Science
دوره 17 شماره
صفحات -
تاریخ انتشار 2016