A graph G with n vertices and maximum degree G cannot be given weak sense of direction using less than G colours. It is known that n colours are always sufficient, and it was conje...
We introduce and discuss generalizations of the problem of independent transversals. Given a graph property R, we investigate whether any graph of maximum degree at most d with a ...
In edge colouring it is often useful to have information about the degree distribution of the neighbours of a given vertex. For example, the well known Vizing's Adjacency Lem...
We introduce the concept of an edge-colouring total k-labelling. This is a labelling of the vertices and the edges of a graph G with labels 1, 2, . . . , k such that the weights o...
: We present an improved upper bound of O(d1+ 1 m−1 ) for the (2, F)-subgraph chromatic number χ2,F (G) of any graph G of maximum degree d. Here, m denotes the minimum number of...