... digraph, i.e., each directed edge has an opposite directed edge, then the weak
colouring game on G and the weak game chromatic number of G defined coincide with
the definition of the colouring game ... game chromatic number of undirected graph
G (by viewing each pair of opposite directed edges as a n undirected edge).
For a digraph D, the underlying graph of D is an undirected graph D...
... L).
A function f : V → N is an L -colouring of G if f is a colouring of G with the
additional requirement that f (v) ∈ L(v) for all v ∈ V (G). If G admits an L -colouring,
then G is said to be L-colourable.
The ... references on graph colouring
games and L-colourings can be found e.g. in [17].
In this paper we are interested in another version of this game. We combine concepts
of game a...
... have appeared in the literature,
and some of them have been arranged to work in the context of directed graphs, cf. [15].
We propose a few more, in particular in hypergraphs. They are related ... number, Electron. J. Combin.
8 (2001) #R14, 13pp.
[16] J. Wu, X. Zhu, Lower bounds for the game colouring number of partial k-trees and
planar graphs, manuscript 2003.
[17] X. Zhu, Game coloring
... in this note are undirected graphs, without loops and mul-
tiple edges, containing no isolated points. We use the arrow notation of Rado, writing
J → (G, H) whenever each colouring of edges of
... vertex
for each group element. Vertices corresponding to group elements u and v
are joined by a directed colored edge labeled g precisely if ug = v.Agraph
is obtained by replacing the colored
... receive the same color in both colorings.
1 Introduction
All graphs considered here are finite, undirected, and have no loops or multiple edges. For
the standard graph-theoretic and design-theoretic
... T
r
be a family of trees with vertices of degree not exceeding 3, each tree
with a given edge-3 -colouring. Let P =(P
r
) be the family of cubic Cayley graphs
defined by the corresponding involutory ... ,α
k
},the
vertex v is adjacent to the vertices α
1
v, α
2
v, ,α
k
v. Note that the edge joining v
and w is undirected, because S is closed under inversion, and hence wv
−1
is in S
if and only...