グラフアルゴリズムの効率化と評価に関する研究

平成13年度-平成14年度科学研究費補助金(基盤研究(C)(2))研究成果報告書,課題番号.1367038

Multicoloring of graphs to secure a secret

Vertex coloring and multicoloring of graphs are a well known subject in graph theory, as well as their applications. In vertex multicoloring, each vertex is assigned some subset of a given set of colors. Here we propose a new kind of vertex multicoloring, motivated by the situation of sharing a secret and securing it from the actions of some number of attackers. We name the multicoloring a highly a-resistant vertex k-multicoloring, where a is the number of the attackers, and k the number of colors. For small values a we determine what is the minimal number of vertices a graph must have in order to allow such a coloring, and what is the minimal number of colors needed