## Abstract We introduce the circular chromatic number Ο~__c__~ of a digraph and establish various basic results. They show that the coloring theory for digraphs is similar to the coloring theory for undirected graphs when independent sets of vertices are replaced by acyclic sets. Since the directe
Two results on the digraph chromatic number
β Scribed by Ararat Harutyunyan; Bojan Mohar
- Book ID
- 113567592
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 191 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
## Abstract The circular chromatic number is a refinement of the chromatic number of a graph. It has been established in [3,6,7] that there exists planar graphs with circular chromatic number __r__ if and only if __r__ is a rational in the set {1}ββͺβ[2,4]. Recently, Mohar, in [1,2] has extended the
Hilton, A.J.W., Recent results on the total chromatic number, Discrete Mathematics 111 (1993) 323-331. We give a survey of various recent results concerning the total chromatic number of simple graphs.
The mean chromatic number of a graph is a measure of the expected performance of the greedy vertex-colouring algorithm when each ordering of the vertices is equally likely. Some results on the value of the mean chromatic number and its asymptotic behaviour are presented.