Vectorial solutions to list multicoloring problems on graphs

Abstract : 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.
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Advances and Applications in Discrete Mathematics, Pushpa Publishing House, 2012, Volume 9 (Numéro 2), pp 65 --81
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  • HAL Id : hal-00672373, version 1
  • ARXIV : 1202.4842

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Yves Aubry, Jean-Christophe Godin, Olivier Togni. Vectorial solutions to list multicoloring problems on graphs. Advances and Applications in Discrete Mathematics, Pushpa Publishing House, 2012, Volume 9 (Numéro 2), pp 65 --81. 〈hal-00672373〉

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