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 Vectorial solutions to list multicoloring problems on graphs


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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 {\sl channel assignment problem}. Furthermore, we describe the set of solutions to the {\sl on call problem}: when $w$ is not a permissible weight, we find all the nearest permissible weights $w$. Finally, we give a solution to the non-recoloring problem keeping a given subcoloring.



Author: Yves Aubry; Jean-Christophe Godin; Olivier Togni

Source: https://archive.org/







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