… In this note we study a problem on vertex list colouring of … its vertex set, and suppose each v
∈ V(G) is assigned a list S(v) … We say that a vertex colouring f of G is a proper list colouring of …

… If L is a list-assignment to G, then an L-colouring of G is a colouring (not necessarily proper)
… each vertex receives a colour from its own list; we talk loosely of colouring G from its lists. …

… colouring y and z with colour 1, and then the vertices of T by the greedy heuristic as above,
ending with the root x, we obtain a ∆-colouring … latter expression to list colourings, we need an …

… of the list colouring problem: on-line list colouring of graphs. List assignments and colourings
of … We assume that the list of permissible colours for each vertex is a set of positive integers. …

… Defining sets of vertex colourings are closely related to the list colouring of a graph. In a
list colouring for each vertex v there is a given list of colours 5% allowable on that vertex. …

… If, instead of colouring every vertex with a colour from the same set [k] = {t, 2, ..… vertex x be
chosen from a special set or list L(x) assigned to x, then we arrive at the concept of list colouring…

… every vertex whose list admits a unique colour (that is, a colour that does not appear on the
list of any other vertex of C) with such a colour, and then colour the remaining vertices via a …

… the following result about vertex list colourings, which shows … the sets of lists SšvŽ; satisfying
that for every vertex jSšvŽj ¼ … their list is at most d: Then there exists a proper colouring of …

… List colourings of the vertices of a graph G are a generalization of the wellknown vertex
colouring of G. Therefore, it is logical to ask about the relationship between the chromatic number …

… colouring concepts and results in the literature. Here our focus is to survey results on vertex
colourings … the problem of colouring the edges of a graph, instead of the vertices, in such a …