Beisegel, Jesse and Denkert, Carolin and Köhler, Ekkehard and Krnc, Matjaž and Pivač, Nevenaet al. - On the End-Vertex Problem of Graph Searches

dmtcs:4937 - Discrete Mathematics & Theoretical Computer Science, June 13, 2019, vol. 21 no. 1, ICGT 2018
On the End-Vertex Problem of Graph Searches

Authors: Beisegel, Jesse and Denkert, Carolin and Köhler, Ekkehard and Krnc, Matjaž and Pivač, Nevena and Scheffler, Robert and Strehler, Martin

End vertices of graph searches can exhibit strong structural properties and are crucial for many graph algorithms. The problem of deciding whether a given vertex of a graph is an end-vertex of a particular search was first introduced by Corneil, Köhler and Lanlignel in 2010. There they showed that this problem is in fact NP-complete for LBFS on weakly chordal graphs. A similar result for BFS was obtained by Charbit, Habib and Mamcarz in 2014. Here, we prove that the end-vertex problem is NP-complete for MNS on weakly chordal graphs and for MCS on general graphs. Moreover, building on previous results, we show that this problem is linear for various searches on split and unit interval graphs.


Source : oai:arXiv.org:1810.12253
Volume: vol. 21 no. 1, ICGT 2018
Published on: June 13, 2019
Submitted on: October 31, 2018
Keywords: Computer Science - Discrete Mathematics


Share