Pathwidth and Searching in Parameterized Threshold Graphs
Treewidth and pathwidth are important graph parameters that represent how close the graph is to trees and paths respectively. We calculate treewidth and pathwidth on parameterized chordal and threshold graphs. We define a chordal + 1v graph as a graph that can be made into a chordal graph by removing a vertex. We give polynomial time algorithms for computing the treewidth of a chordal + 1v graph, pathwidth of a threshold + 1v graph and a threshold + 2e graph. The mixed search number of a graph is the minimum number of cops required to capture a single robber, who is hiding in the graph. We apply the algorithm to compute the pathwidth in order to compute the mixed search number of a threshold + 1v graph.
KeywordsGraph searching treewidth pathwidth parameterization threshold graphs
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