arXiv subjects

Aljoša Šubašić

Publications and source records attributed to Aljoša Šubašić.

4 recordsLinked to original sources

arXiv2026

Results on Cartesian $1$-capacity of graphs

The concept of graph capacity extends graph span by considering the maximum number of agents that can simultaneously traverse a graph while preserving a prescribed minimum distance. We study the Cartesian $1$-capacity, corresponding to the movement in which exactly one agent moves at each step. We establish general lower and upper bounds based on structural graph properties and derive exact results for trees. Our work highlights the role of branching and bridge structures in determining the Cartesian $1$-capacity and provides new insights into collision-free multi-agent motion on graphs.

math.CO↗

arXiv2026

Span capacities of graphs

The $d$-capacity of a graph $G$ is introduced as the maximum number of players that can simultaneously traverse $G$ such that each player visits all vertices while maintaining a distance of at least $d$ under various movement rules. We determine their values for paths and cycles and provide bounds for bipartite graphs. Furthermore, we characterize topfull graphs, where the 1-capacities reach their theoretical maximum, establishing a connection to graph factorizations and connectivity.

math.CO↗

arXiv2025

The relation between different edge spans of a graph

In several recent papers, the maximal safety distance that two players can maintain while moving through a graph has been defined and studied using three different spans of the graph, each with different movement conditions. Mainly, vertex spans have been studied, in which players visit all the vertices of a graph. In this paper, we analyze the values of three edge spans, which represent the maximal safety distance that two players can maintain while visiting all the edges of a graph. We present edge span values for some graph classes and examine the relationship between different variants of edge spans.

math.CO↗

arXiv2023

Vertex spans of multilayered cycles

In this paper we are defining a special class of graphs called multilayered graphs and its subclass, multilayered cycles. For that subclass of graphs we are giving the values of all vertex spans (strong, direct, or Cartesian span). Surprisingly, our results reveal that, irrespective of the chosen movement rules, the span values only depend on the length of the individual cycles, not the number of layers, which holds significant implications.

math.CO↗