We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
Colouring a graph with its chromatic number of colours is known to be NP-hard. Identifying an algorithm in which descisions are made locally with no information about the graph...
We characterize the edge-signed graphs in which every 'significant' positive closed walk (or combination of walks) has even length, under seven different criteria for si...
We prove that for every k and every ε > 0, there exists g such that every graph with tree-width at most k and odd-girth at least g has circular chromatic number at most 2 + ε...