Note on graphs colouring
نویسندگان
چکیده
منابع مشابه
On Edge-colouring Indiierence Graphs on Edge-colouring Indiierence Graphs
Vizing's theorem states that the chromatic index 0 (G) of a graph G is either the maximum degree (G) or (G) + 1. A graph G is called overfull if jE(G)j > (G)bjV (G)j=2c. A suu-cient condition for 0 (G) = (G)+1 is that G contains an overfull subgraph H with (H) = (G). Plantholt proved that this condition is necessary for graphs with a universal vertex. In this paper, we conjecture that, for indi...
متن کاملOn Edge-Colouring Indifference Graphs
Vizing's theorem states that the chromatic index 0 (G) of a graph G is either the maximum degree (G) or (G) + 1. A graph G is called overfull if jE(G)j > (G)bjV (G)j=2c. A suucient condition for 0 (G) = (G) + 1 is that G contains an overfull subgraph H with (H) = (G). Plantholt proved that this condition is necessary for graphs with a universal vertex. In this paper, we conjecture that, for ind...
متن کاملOn Colouring Point Visibility Graphs
In this paper we show that it can be decided in polynomial time whether or not the visibility graph of a given point set is 4-colourable, and such a 4-colouring, if it exists, can also be constructed in polynomial time. We show that the problem of deciding whether the visibility graph of a point set is 5-colourable, is NP-complete. We give an example of a point visibility graph that has chromat...
متن کاملOn the Edge-colouring of Split Graphs on the Edge-colouring of Split Graphs
We consider the following question: can split graphs with odd maximum degree be edge-coloured with maximum degree colours? We show that any odd maximum degree split graph can be transformed into a special split graph. For this special split graph, we were able to solve the question, in case the graph has a quasi-universal vertex.
متن کاملColouring graphs with bounded generalized colouring number
Given a graph G and a positive integer p, χp(G) is the minimum number of colours needed to colour the vertices of G so that for any i ≤ p, any subgraph H of G of tree-depth i gets at least i colours. This paper proves an upper bound for χp(G) in terms of the k-colouring number colk(G) of G for k = 2p−2. Conversely, for each integer k, we also prove an upper bound for colk(G) in terms of χk+2(G)...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 1992
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.1992.125898