Token Sliding on Chordal Graphs

Let I be an independent set of a graph G. Imagine that a token is located on every vertex of I. We can now move the tokens of I along the edges of the graph as long as the set of tokens still defines an independent set of G. Given two independent sets I and J, the Token Sliding problem consists in deciding whether there exists a sequence of independent sets which transforms I into J so that every pair of consecutive independent sets of the sequence can be obtained via a single token move. This problem is known to be PSPACE-complete even on planar graphs.

[1]  Daniël Paulusma,et al.  Kempe equivalence of colourings of cubic graphs , 2015, Eur. J. Comb..

[2]  Takehiro Ito,et al.  Fixed-Parameter Tractability of Token Jumping on Planar Graphs , 2014, ISAAC.

[3]  Paul S. Bonsma,et al.  Reconfiguring Independent Sets in Claw-Free Graphs , 2014, SWAT.

[4]  Daniël Paulusma,et al.  A Reconfigurations Analogue of Brooks' Theorem and Its Consequences , 2016, J. Graph Theory.

[5]  Ryuhei Uehara,et al.  Shortest Reconfiguration of Sliding Tokens on a Caterpillar , 2016, WALCOM.

[6]  Takehiro Ito,et al.  On the complexity of reconfiguration problems , 2008, Theor. Comput. Sci..

[7]  Yota Otachi,et al.  Polynomial-Time Algorithm for Sliding Tokens on Trees , 2014, ISAAC.

[8]  Jan van den Heuvel,et al.  The complexity of change , 2013, Surveys in Combinatorics.

[9]  Paul S. Bonsma,et al.  The complexity of rerouting shortest paths , 2010, Theor. Comput. Sci..

[10]  Marthe Bonamy,et al.  Reconfiguring Independent Sets in Cographs , 2014, ArXiv.

[11]  Marthe Bonamy,et al.  On a conjecture of Mohar concerning Kempe equivalence of regular graphs , 2015, J. Comb. Theory B.

[12]  Naomi Nishimura,et al.  On the Parameterized Complexity of Reconfiguration Problems , 2013, Algorithmica.

[13]  Erik D. Demaine,et al.  PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation , 2002, Theor. Comput. Sci..

[14]  Takehiro Ito,et al.  On the Parameterized Complexity for Token Jumping on Graphs , 2014, TAMC.

[15]  Paul S. Bonsma.  Independent Set Reconfiguration in Cographs , 2014, WG.

[16]  Kellogg S. Booth,et al.  Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms , 1976, J. Comput. Syst. Sci..

[17]  Christos H. Papadimitriou,et al.  The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies , 2006, SIAM J. Comput..

[18]  Jörg Flum,et al.  Parameterized Complexity Theory , 2006, Texts in Theoretical Computer Science. An EATCS Series.

[19]  Frank Harary,et al.  Graph Theory , 2016 .

[20]  Martin Milanic,et al.  Complexity of independent set reconfigurability problems , 2012, Theor. Comput. Sci..

[21]  Marthe Bonamy,et al.  Recoloring bounded treewidth graphs , 2013, Electron. Notes Discret. Math..