We study vertex-colorings of plane graphs that do not contain a rainbow face, i.e., a face with vertices of mutually distinct colors. If G is a 3-connected plane graph with n vert...
The problem of computing the chromatic number of a P5-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show tha...
It is proven that for every fixed h, a and b, a graph with n vertices and minimum degree at least h-1 h n, which contains no copy of Kb (the complete graph with b vertices), conta...
We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time,...
Let G be a median graph on n vertices and m edges and let k be the number of equivalence classes of the Djokovi´c’s relation Θ defined on the edge-set of G. Then 2n − m −...
Sandi Klavzar, Henry Martyn Mulder, Riste Skrekovs...