Wang and Lih conjectured that for every g 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree M(g) is (+1)-colorable. ...
The square G2 of a graph G is the graph with the same vertex set as G and with two vertices adjacent if their distance in G is at most 2. Thomassen showed that for a planar graph ...
Jeager et al introduced a concept of group connectivity as an generalization of nowhere zero flows and its dual concept group coloring, and conjectured that every 5-edge connected...
A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...