2019
DOI: 10.1007/978-3-030-19955-5_12
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Minimizing Branching Vertices in Distance-Preserving Subgraphs

Abstract: It is NP-hard to determine the minimum number of branching vertices needed in a singlesource distance-preserving subgraph of an undirected graph. We show that this problem can be solved in polynomial time if the input graph is an interval graph.In earlier work, it was shown that every interval graph with k terminal vertices admits an all-pairs distance-preserving subgraph with O(k log k) branching vertices [GR17a]. We consider graphs that can be expressed as the strong product of two interval graphs, and prese… Show more

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