2,447 research outputs found
On the phase transitions of graph coloring and independent sets
We study combinatorial indicators related to the characteristic phase
transitions associated with coloring a graph optimally and finding a maximum
independent set. In particular, we investigate the role of the acyclic
orientations of the graph in the hardness of finding the graph's chromatic
number and independence number. We provide empirical evidence that, along a
sequence of increasingly denser random graphs, the fraction of acyclic
orientations that are `shortest' peaks when the chromatic number increases, and
that such maxima tend to coincide with locally easiest instances of the
problem. Similar evidence is provided concerning the `widest' acyclic
orientations and the independence number
Vectorial solutions to list multicoloring problems on graphs
For a graph with a given list assignment on the vertices, we give an
algebraical description of the set of all weights such that is
-colorable, called permissible weights. Moreover, for a graph with a
given list and a given permissible weight , we describe the set of all
-colorings of . By the way, we solve the {\sl channel assignment
problem}. Furthermore, we describe the set of solutions to the {\sl on call
problem}: when is not a permissible weight, we find all the nearest
permissible weights . Finally, we give a solution to the non-recoloring
problem keeping a given subcoloring.Comment: 10 page
A polyhedral approach for the Equitable Coloring Problem
In this work we study the polytope associated with a 0,1-integer programming
formulation for the Equitable Coloring Problem. We find several families of
valid inequalities and derive sufficient conditions in order to be
facet-defining inequalities. We also present computational evidence that shows
the efficacy of these inequalities used in a cutting-plane algorithm
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