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- Type of Document: Article
- Publisher: 2008
- Abstract:
- In this paper, first we introduce the concept of a connected graph homomorphism as a homomorphism for which the inverse image of any edge is either empty or a connected graph, and then we concentrate on chromatically connected (resp. chromatically disconnected) graphs such as G for which any χ(G)-colouring is a connected (resp. disconnected) homomorphism to K χ(G). In this regard, we consider the relationships of the new concept to some other notions as uniquely-colourability. Also, we specify some classes of chromatically disconnected graphs such as Kneser graphs KG(m, n) for which m is sufficiently larger than n, and the line graphs of non-complete class II graphs. Moreover, we prove that the existence problem for connected homomorphisms to any fixed complete graph is an NP-complete problem
- Keywords:
- Connectivity ; Graph colouring ; Uniquely-colourable graphs
- Source: Ars Combinatoria ; Volume 89 , 2008 , Pages 115-126 ; 03817032 (ISSN)