### Vectorial solutions to list multicoloring problems on graphs [article]

Yves Aubry, Olivier Togni
<span title="2012-02-22">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For a graph G with a given list assignment L on the vertices, we give an algebraical description of the set of all weights w such that G is (L,w)-colorable, called permissible weights. Moreover, for a graph G with a given list L and a given permissible weight w, we describe the set of all (L,w)-colorings of G. By the way, we solve the channel assignment problem. Furthermore, we describe the set of solutions to the on call problem: when w is not a permissible weight, we find all the nearest
more &raquo; ... ssible weights w'. Finally, we give a solution to the non-recoloring problem keeping a given subcoloring.
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