3 papers
math.CO2026
Fourteen and fifteen lonely runners
Jaan Allikvere
We prove the Lonely Runner Conjecture for fourteen and fifteen runners. Our proof combines a stronger bound on the speed product in a primitive counterexample with exhaustive compu…
math.CO2026
The edge multiset dimension of hypercubes
Jaan Allikvere
For a graph G and a nonempty set S of vertices, the edge multiset representation of an edge e is the multiset of distances from e to the elements of S, where d(uv,s)=min{d(u,s),d(v…
math.CO2026
The Multiset Dimension of Graphs: Extremal Values and King Grids
Jaan Allikvere
We present three results on the multiset dimension of graphs, resolving one conjecture and two open questions from the literature. First, we disprove the conjecture of Simanjuntak,…