A note on selective line-graphs and partition colorings

Abstract We extend a one-to-one correspondence between the set of all colorings of any graph and the set of all stable sets of an auxiliary graph, from graphs to partitioned graphs. This correspondence has an application to Selective Coloring and to Selective Max-Coloring.

[1]  Marc Demange,et al.  On some applications of the selective graph coloring problem , 2015, Eur. J. Oper. Res..

[2]  Gintaras Palubeckis.  On the recursive largest first algorithm for graph colouring , 2008, Int. J. Comput. Math..

[3]  Petrica C. Pop,et al.  On the complexity of the selective graph coloring problem in some special classes of graphs , 2014, Theor. Comput. Sci..

[4]  Vincent Jost,et al.  A one-to-one correspondence between colorings and stable sets , 2008, Oper. Res. Lett..

[5]  William J. Cook,et al.  Maximum-weight stable sets and safe lower bounds for graph coloring , 2012, Mathematical Programming Computation.

[6]  Marc Demange,et al.  On the Minimum and Maximum Selective Graph Coloring Problems , 2015, CTW.

[7]  Flavia Bonomo,et al.  A note on the Cornaz-Jost transformation to solve the graph coloring problem , 2013, Inf. Process. Lett..

[8]  Fabio Furini,et al.  Solving Vertex Coloring Problems as Maximum Weighted Stable Set Problems , 2017, CTW.

[9]  Fabio Furini,et al.  An exact algorithm for the Partition Coloring Problem , 2018, Comput. Oper. Res..

[10]  Celso C. Ribeiro,et al.  Routing and wavelength assignment by partition colouring , 2006, Eur. J. Oper. Res..

[11]  Gintaras Palubeckis.  Facet-inducing web and antiweb inequalities for the graph coloring polytope , 2010, Discret. Appl. Math..

[12]  Cid C. de Souza,et al.  A branch-and-price approach for the partition coloring problem , 2011, Oper. Res. Lett..

[13]  Bernard Ries,et al.  Perfectness of clustered graphs , 2013, Discret. Optim..

[14]  Leah Epstein,et al.  Weighted Sum Coloring in Batch Scheduling of Conflicting Jobs , 2006, Algorithmica.

[15]  Denis Cornaz,et al.  Chromatic Gallai identities operating on Lovász number , 2014, Math. Program..

[16]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .