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math.CO2026
Four colours are needed for closed-neighbourhood conflict-free colouring of all planar graphs
Jelena Sedlar, Riste Škrekovsk
A colouring of the vertices of a graph is conflict-free with respect to closed neighbourhoods if every closed neighbourhood contains a colour that appears on exactly one of its ver…
math.CO2026
Counting geodesic paths in graphs
Martin Knor, Jelena Sedlar, Riste Škrekovski +1
A geodesic is a shortest path which connects a pair of vertices of a graph G. In this paper we define the geodesic subpath number gpn(G) of a graph G as the number of geodesics in…