On end-vertices of Lexicographic Breadth First Searches

Recently Lexicographic Breadth First Search (LBFS) has received considerable attention and has often been employed in a multi-sweep fashion. One variant of LBFS called LBFS+ breaks ties by choosing the last vertex of the tied set in a previous LBFS. This has motivated the study of vertices that may appear last in an LBFS (called end-vertices). In this paper, we present various theoretical and algorithmic results concerning end-vertices.

[1]  Feodor F. Dragan,et al.  Diameter determination on restricted graph families , 1998, Discret. Appl. Math..

[2]  Klaus Simon.  A New Simple Linear Algorithm to Recognize Interval Graphs , 1991, Workshop on Computational Geometry.

[3]  Dieter Kratsch,et al.  Domination on Cocomparability Graphs , 1993, SIAM J. Discret. Math..

[4]  Stephan Olariu,et al.  The ultimate interval graph recognition algorithm? , 1998, SODA '98.

[5]  Feodor F. Dragan,et al.  Almost Diameter of a House-hole-free Graph in Linear Time Via LexBFS , 1999, Discret. Appl. Math..

[6]  Derek G. Corneil,et al.  Lexicographic Breadth First Search - A Survey , 2004, WG.

[7]  Feodor F. Dragan,et al.  LexBFS-Orderings and Power of Graphs , 1996, WG.

[8]  Stephan Olariu,et al.  Linear Time Algorithms for Dominating Pairs in Asteroidal Triple-free Graphs , 1995, SIAM J. Comput..

[9]  Derek G. Corneil,et al.  A Unified View of Graph Searching , 2008, SIAM J. Discret. Math..

[10]  Stephan Olariu,et al.  The LBFS Structure and Recognition of Interval Graphs , 2009, SIAM J. Discret. Math..

[11]  C. Lekkeikerker,et al.  Representation of a finite graph by a set of intervals on the real line , 1962 .

[12]  Laurent Viennot,et al.  Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing , 2000, Theor. Comput. Sci..

[13]  Robert E. Tarjan,et al.  Algorithmic Aspects of Vertex Elimination on Graphs , 1976, SIAM J. Comput..

[14]  Feodor F. Dragan,et al.  LexBFS-orderings and powers of chordal graphs , 1997, Discret. Math..