## Abstract A (finite or infinite) graph __G__ is __constructible__ if there exists a wellβordering β€ of its vertices such that for every vertex __x__ which is not the smallest element, there is a vertex __y__ < __x__ which is adjacent to __x__ and to every neighbor __z__ of __x__ with __z__ < __x_
Median graphs and Helly hypergraphs
β Scribed by H.M. Mulder; A. Schrijver
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 963 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In addition to a widely studied notion of homomorphisms of graphs and hypergraphs, [2, 5 , 6, 7, 9, 13, 141, we introduce the dual notion of cohomomorphisms. We shall concentrate on only a few aapects of these mappings, mostly with regard to intended applications, [lo, 111. Our basic motivation is t
Ftiredi, Z&an, Indecomposable regular graphs and hypergraphs, Discrete Mathematics 101 (1992) 59-64. Let G be a d-regular simple graph with n vertices. Here it is proved that for d > 6 -1, G contains a proper regular spanning subhypergraph. The same statement is proved for multigraphs with d > (n -1
Given a graph property P, graph G and integer k 20, a P k-colouring of G is a function Jr:V(G)+ (1,. . ) k} such that the subgraph induced by each colour class has property P. When P is closed under induced subgraphs, we can construct a hypergraph HG such that G is P k-colourable iff Hg is k-colou
## Abstract The nβcube is characterized as a connected regular graph in which for any three vertices __u, v__, and __w__ there is a unique vertex that lies simultaneously on a shortest (__u, v__)βpath, a shortest (__v, w__)βpath, and a shortest (__w, u__)βpath.
A notion of parallelism is defined in finite median graphs and a number of properties about geodesics and the existence of cubes are obtained. Introducing sites as a double structure of partial order and graph on a set, it is shown that all median graphs can be constructed from sites and, in fact, t