A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph (G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k-cr
On the construction of 3-chromatic hypergraphs with few edges
β Scribed by Gebauer, Heidi
- Book ID
- 120297014
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 245 KB
- Volume
- 120
- Category
- Article
- ISSN
- 0097-3165
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## Abstract Let __K(p, q), p β€ q__, denote the complete bipartite graph in which the two partite sets consist of __p__ and __q__ vertices, respectively. In this paper, we prove that (1) the graph __K(p, q)__ is chromatically unique if __p__ β₯ 2; and (2) the graph __K(p, q)__ β __e__ obtained by del
For some families of graphs of simplicial 3-polytopes with two types of edges structural properties are described, for other ones their cardinality is determined. ## 1. ln~oduction Griinbaum and Motzkin [3], Griinbaum and Zaks [4], and Malkevitch [6] investigated the structural properties of triva