图的列表多色问题的向量解
Vectorial solutions to list multicoloring problems on graphs
摘要：
对于一个图$G$，给定列表分配$L$的顶点，我们给出了一个代数描述的所有权重$w$，使$G$是$(L,w)$ -着色，称为允许的重量。此外，对于一个图$G$与一个给定的列表$L$和一个给定的允许重量$w$，我们描述了所有的$(L,w)$ -着色的$G$的集合。顺便说一下，我们解决了{ \sl信道分配问题}。此外，我们描述了一组解决方案{ \sl呼叫问题}：当$w$是不是一个允许的权重，我们找到所有最近的允许的权重$w'$。最后，我们给出了保持给定子染色的非包围问题的一个解决方案。
英文摘要：
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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