A dichotomy for the dominating set problem for classes defined by small forbidden induced subgraphs

We completely determine the complexity status of the dominating set problem for hereditary graph classes defined by forbidden induced subgraphs with at most five vertices.

[1]  J. A. Bondy,et al.  Graph Theory , 2008, Graduate Texts in Mathematics.

[2]  Vadim V. Lozin,et al.  Boundary properties of the satisfiability problems , 2013, Inf. Process. Lett..

[3]  Vadim V. Lozin,et al.  Boundary classes of graphs for the dominating set problem , 2004, Discrete Mathematics.

[4]  Petr A. Golovach,et al.  List Coloring in the Absence of Two Subgraphs , 2013, CIAC.

[5]  Vadim V. Lozin,et al.  Independent sets in extensions of 2K2-free graphs , 2005, Discret. Appl. Math..

[6]  Vadim V. Lozin,et al.  Boundary properties of graphs for algorithmic graph problems , 2011, Theor. Comput. Sci..

[7]  Malyshev Dmitriy,et al.  The complexity of the edge 3-colorability problem for graphs without two induced fragments each on at most six vertices , 2014 .

[8]  D. V. Korobitsin,et al.  On the complexity of domination number determination in monogenic classes of graphs , 1992 .

[9]  V. E. Alekseev,et al.  On easy and hard hereditary classes of graphs with respect to the independent set problem , 2003, Discret. Appl. Math..

[10]  Dmitriy S. Malyshev,et al.  The complexity of the 3-colorability problem in the absence of a pair of small forbidden induced subgraphs , 2015, Discret. Math..

[11]  Vadim V. Lozin,et al.  NP-hard graph problems and boundary classes of graphs , 2007, Theor. Comput. Sci..

[12]  Zsolt Tuza,et al.  Complexity of Coloring Graphs without Forbidden Induced Subgraphs , 2001, WG.

[13]  Dmitriy S. Malyshev,et al.  Two cases of polynomial-time solvability for the coloring problem , 2016, J. Comb. Optim..

[14]  Vadim V. Lozin,et al.  Independent domination in finitely defined classes of graphs: Polynomial algorithms , 2015, Discret. Appl. Math..

[15]  Dmitriy S. Malyshev,et al.  The coloring problem for {P5, P̅5}-free graphs and {P5, Kp-e}-free graphs is polynomial , 2015, ArXiv.

[16]  Dmitriy S. Malyshev,et al.  The coloring problem for classes with two small obstructions , 2013, Optim. Lett..

[17]  Jian Song,et al.  4-Coloring H-Free Graphs When H Is Small , 2012, SOFSEM.

[18]  Daniel Lokshtanov,et al.  Independent Set in P5-Free Graphs in Polynomial Time , 2014, SODA.

[19]  Russell Merris,et al.  Split graphs , 2003, Eur. J. Comb..

[20]  Vadim V. Lozin,et al.  Vertex coloring of graphs with few obstructions , 2017, Discret. Appl. Math..

[21]  Dmitriy S. Malyshev,et al.  A complexity dichotomy and a new boundary class for the dominating set problem , 2016, J. Comb. Optim..

[22]  D. Malyshev,et al.  Classes of graphs critical for the edge list-ranking problem , 2014, Journal of Applied and Industrial Mathematics.

[23]  Jian Song,et al.  Updating the complexity status of coloring graphs without a fixed induced linear forest , 2012, Theor. Comput. Sci..

[24]  Dmitriy S. Malyshev,et al.  Boundary graph classes for some maximum induced subgraph problems , 2014, J. Comb. Optim..