arXiv subjects

Tanja Vojkovic

Publications and source records attributed to Tanja Vojkovic.

3 recordsLinked to original sources

arXiv2023

Graph multicoloring in solving node malfunction and attacks in a secret-sharing network

We observe a network scenario where parts of a secret are distributed among its nodes. Within the network, a group of attackers is actively trying to obtain the complete secret, while there is also the issue of some nodes malfunctioning or being absent. In this paper, we address this problem by employing graph multicoloring techniques, focusing on the case of a single attacker and varying numbers of malfunctioning nodes.

math.CO↗

arXiv2022

Some considerations on the maximal safety distance in a graph

The work in this paper is motivated by I. Banič's and A. Taranenko's recent paper, where they introduced a new notion, the span of a graph. Their goal was to solve the problem of keeping a safety distance while two actors are moving through a graph and they present three different types of graph spans, depending on the movement rules. We observe the same goal, but give a different approach to that problem by directly defining the maximal safety distance for different movement rules two actors can take. This allowed us to solve several problems, prove some relations between different graph spans and calculate the span values for some classes of graphs.

math.CO↗

arXiv2018

Safe 3-coloring of graphs

The applications of graph coloring are diverse and many so lots of new types of coloring are being proposed and explored. Here we define a safe k-coloring, motivated by the application of coloring to secret sharing. Secret sharing is a way of securing a secret from a number of attackers by dividing it into parts and then distributing those parts to some persons, represented here by graph vertices. Parts of the secret are represented by colors which are then assigned to the vertices under certain conditions, making a coloring safe if a predetermined number of attackers cannot read the whole secret, nor disable the rest of the group from doing so. We observe a fixed number of colors, namely 3, and analyze what kind of graphs have a safe 3-coloring.

math.CO↗