The complexity of independent set reconfiguration on bipartite graphs

We settle the complexity of the Independent Set Reconfiguration problem on bipartite graphs under all three commonly studied reconfiguration models. We show that under the token jumping or token addition/removal model the problem is NP-complete. For the token sliding model, we show that the problem remains PSPACE-complete.

[1]  Naomi Nishimura,et al.  Shortest Reconfiguration Paths in the Solution Space of Boolean Formulas , 2017, SIAM J. Discret. Math..

[2]  P. Hall.  On Representatives of Subsets , 1935 .

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

[4]  Naomi Nishimura,et al.  Vertex Cover Reconfiguration and Beyond , 2014, ISAAC.

[5]  Jan van den Heuvel,et al.  Connectedness of the graph of vertex-colourings , 2008, Discret. Math..

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

[7]  Michal Pilipczuk,et al.  Parameterized Algorithms , 2015, Springer International Publishing.

[8]  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..

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

[10]  Ge Xia,et al.  Flip Distance Is in FPT Time O(n+ k * c^k) , 2015, STACS.

[11]  Takehiro Ito,et al.  Reconfiguration of list edge-colorings in a graph , 2012, Discret. Appl. Math..

[12]  Marthe Bonamy,et al.  Token Sliding on Chordal Graphs , 2016, WG.

[13]  Richard C. Brewster,et al.  A dichotomy theorem for circular colouring reconfiguration , 2015, Theor. Comput. Sci..

[14]  Takehiro Ito,et al.  On the complexity of reconfiguration problems , 2011, Theor. Comput. Sci..

[15]  Yota Otachi,et al.  Sliding Token on Bipartite Permutation Graphs , 2015, ISAAC.

[16]  Hans L. Bodlaender,et al.  A Tourist Guide through Treewidth , 1993, Acta Cybern..

[17]  Dimitrios M. Thilikos,et al.  Treewidth for Graphs with Small Chordality , 1997, Discret. Appl. Math..

[18]  Fahad Panolan,et al.  Reconfiguration on Sparse Graphs , 2015, WADS.

[19]  Ryuhei Uehara,et al.  Sliding Tokens on a Cactus , 2016, ISAAC.

[20]  Graham Kendall,et al.  A Survey of NP-Complete Puzzles , 2008, J. Int. Comput. Games Assoc..

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

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

[23]  Robin Thomas,et al.  Graph Searching and a Min-Max Theorem for Tree-Width , 1993, J. Comb. Theory, Ser. B.

[24]  Paul D. Seymour,et al.  Graph minors. III. Planar tree-width , 1984, J. Comb. Theory B.

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

[26]  Vinayak Pathak,et al.  Flip Distance Between Two Triangulations of a Point Set is NP-complete , 2012, CCCG.

[27]  Takehiro Ito,et al.  Reconfiguration of Vertex Covers in a Graph , 2016 .

[28]  Erik D. Demaine,et al.  Geometric folding algorithms - linkages, origami, polyhedra , 2007 .

[29]  W. W. Johnson,et al.  Notes on the "15" Puzzle , 1879 .

[30]  M. Habib,et al.  Treewidth of cocomparability graphs and a new order-theoretic parameter , 1994 .

[31]  Michael R. Fellows,et al.  Crown Structures for Vertex Cover Kernelization , 2007, Theory of Computing Systems.

[32]  Christos H. Papadimitriou,et al.  The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies , 2006, ICALP.

[33]  Marcin Wrochna,et al.  Reconfiguration in bounded bandwidth and tree-depth , 2014, J. Comput. Syst. Sci..

[34]  Ryuhei Uehara,et al.  Polynomial-Time Algorithms for Sliding Tokens on Cactus Graphs and Block Graphs , 2017, ArXiv.

[35]  B. Mohar,et al.  Graph Minors , 2009 .

[36]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[37]  Derek G. Corneil,et al.  Complexity of finding embeddings in a k -tree , 1987 .

[38]  M. Yannakakis.  Computing the Minimum Fill-in is NP^Complete , 1981 .