## 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.
Infinite median graphs, (0, 2)-graphs, and hypercubes
β Scribed by Hans-J. Bandelt; Henry Martyn Mulder
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 450 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Hypercubes are characterized among connected bipartite graphs by interval conditions in several ways. These results are based on the following two facts: (i) connected bipartite graphs are median provided that all their intervals induce median graphs, and (ii) median (0, 2)graphs are hypercubes. No cardinality restrictions are made.
π SIMILAR VOLUMES
A median graph is called compact if it does not contain an isometric ray. This property is shown to be equivalent to the finite intersection property for convex sets. We show that a compact median graph contains a finite cube that is fixed by all of its automorphisms, and that each family of commuti
We consider the problem of embedding graphs into hypercubes with minimal congestion. Kim and Lai showed that for a given N-vertex graph G and a hypercube it is NP-complete to determine whether G is embeddable in the hypercube with unit congestion, but G can be embedded with unit congestion in a hype
## Abstract We analyze three applications of Ramseyβs Theorem for 4βtuples to infinite traceable graphs and finitely generated infinite lattices using the tools of reverse mathematics. The applications in graph theory are shown to be equivalent to Ramseyβs Theorem while the application in lattice t