Vojković, Tanja; Vukičević, Damir; Zlatić, Vinko
(2018)
Multicoloring of graphs to secure a secret.
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti, 22
(534).
pp. 122.
ISSN 18454100
Abstract
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 aresistant vertex kmulticoloring, 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.
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