Influence of the tie-break rule on the end-vertex problem

End-vertices of a given graph search may have some nice properties, as for example it is well known that the last vertex of Lexicographic Breadth First Search (LBFS) in a chordal graph is simplicial, see Rose, Tarjan and Lueker 1976. Therefore it is interesting to consider if these vertices can be r...

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Bibliographic Details
Published in:Discrete Mathematics and Theoretical Computer Science Vol. 16 no. 2; no. PRIMA 2013; pp. 57 - 72
Main Authors: Charbit, Pierre, Habib, Michel, Mamcarz, Antoine
Format: Journal Article
Language:English
Published: Nancy DMTCS 29.07.2014
Discrete Mathematics & Theoretical Computer Science
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
[math.math-co] mathematics [math]/combinatorics [math.co]
Algorithms
Combinatorics
Computer Science
Data Structures and Algorithms
Discrete Mathematics
Graph theory
Mathematical research
Mathematics
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:End-vertices of a given graph search may have some nice properties, as for example it is well known that the last vertex of Lexicographic Breadth First Search (LBFS) in a chordal graph is simplicial, see Rose, Tarjan and Lueker 1976. Therefore it is interesting to consider if these vertices can be recognized in polynomial time or not, as first studied in Corneil, Köhler and Lanlignel 2010. A graph search is a mechanism for systematically visiting the vertices of a graph. At each step of a graph search, the key point is the choice of the next vertex to be explored. Graph searches only differ by this selection mechanism during which a tie-break rule is used. In this paper we study how the choice of the tie-break in case of equality during the search, for a given graph search including the classic ones such as BFS and DFS, can determine the complexity of the end-vertex problem. In particular we prove a counterintuitive NP-completeness result for Breadth First Search solving a problem raised in Corneil, Köhler and Lanlignel 2010.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2081