Naslov
Multicoloring of graphs to secure a secret

Autori
Vojković, Tanja ; Vukičević Damir ; Zlatić Vinko

Izvornik
Rad Hrvatske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i kemijske znanosti. Matematičke znanosti (1845-4100) 22 (2018), 534; 1-22

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Teorija grafova ; bojanje grafova ; višestruko bojanje
(Graph theory ; graph coloring ; multicoloring ; secret sharing)

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA