An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a graph ...
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...
Sensor networks are meant for sensing and disseminating information about the environment they sense. The criticality of a sensed phenomenon determines it’s importance to the en...
Many NP-hard problems can be solved efficiently when the input is restricted to graphs of bounded tree-width or clique-width. In particular, by the celebrated result of Courcelle,...
Fedor V. Fomin, Petr A. Golovach, Daniel Lokshtano...
Erdos proved that there are graphs with arbitrarily large girth and chromatic number. We study the extension of this for generalized chromatic numbers. Generalized graph coloring d...