1 Introduction List colourings of graphs were introduced independently by Vizing [61], by Erd? os, Rubin and Taylor [15], and, from a slightly di?erent perspective, by Levow [43]. Two excellent articles on them are those by Alon [1] and Tuza [59], and the second of these has ...
J. Harris : List coloring of graphs, Graphs and Combinatorics 1 (1985), 115–127.Bollobás, B., Harris, A.J.: List-colourings of graphs. Graphs Comb. 1 (2), 115–127 (1985) MATHBollobás, B., Harris, A.J. (1985) List-colourings of graphs. Graphs and Combinatorics 1: pp. ...
Connected colouringList colouringVertex colorings of graphs and edge colorings of multigraphs are studied such that elements of each color induce a connected subgraph. The relationship is examined between arising quantitative parameters and other known parameters.V.G. Vizing...
A graph G = G(V, E) is called L-list colourable if there is a vertex colouring of G in which the colour assigned to a vertex v is chosen from a list L(v) associated with this vertex. We say G is k-choosable if all lists L(v) have the cardinality k and G is L-list colou...
Ohba has conjectured \cite{ohb} that if the graph $G$ has $2\chi(G)+1$ or fewer vertices then the list chromatic number and chromatic number of $G$ are equal. In this paper we prove that this conjecture is asymptotically correct. More precisely we obtain
We show that for complete bipartite graphs these conditions are asymptotically nearly sharp in a large part of the parameter space. This has provoked the following. In the setup above, we conjecture that a proper list colouring is always guaranteed if and for any provided and are large enough;...
S Akbari,M Ghanbari,S Jahanbekam - IEEE International Conference on Systems 被引量: 1发表: 2011年 On dynamic coloring of fan graphs A \\\emph{dynamic colouring} of a graph is a proper colouring in which no neighbourhood of a non-leaf vertex is monochromatic. The \\\emph{dynamic colouring...
Our study has taken inspiration from study of the strong chromatic number, and we also explore generalizations of the problem above in the same spirit. 展开 关键词: graph colouring graph packing independent transversals list colouring strong chromatic number TRANSVERSALS GRAPHS NUMBER ...
"Task Colouring" "Opgave farvevalg" "label" "Task Comments" "Opgavekommentarer" "label" "Task date not set" "Opgavedato ikke indstillet" "tooltip" "Task Dependencies" "Opgaveafhængigheder" "dialog" "Task Dependency" "Opgaveafhængighed" "menu" ...
Recently, Alon, Cambie, and Kang introduced asymmetric list coloring of bipartite graphs, where the size of each vertex’s list depends on its part. For complete bipartite graphs, we fix the list sizes of one part and consider the resulting asymptotics, revealing an invariant quantity instrumental...