## DISCRETE MATHEMATICS Many applications of digital image processing now deal with three and more dimensional images. One way of tracing the digital images of n-dimensional continuous spaces is to use molecular spaces and its intersection graphs. Two graphs modeling the same space can be transfor
Some applications of graph contractions
✍ Scribed by László Babai
- Publisher
- John Wiley and Sons
- Year
- 1977
- Tongue
- English
- Weight
- 248 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Results in diverse areas, such as the Nielsen‐Schreier theorem on subgroups of free groups and a proof of A. T. White's conjecture on the genus of subgroups are shown to be immediate consequences of a lemma which has already proved useful in investigating topological properties and automorphism group of graphs.
📜 SIMILAR VOLUMES
In [15] , Thomassen proved that any triangle-free k-connected graph has a contractible edge. Starting with this result, there are several results concerning the existence of contractible elements in k-connected graphs which do not contain specified subgraphs. These results extend
We define the (elementary) binary contraction Gs of a graph G = (V, E) in the following way: if (S) is an induced K,,, not contained into an induced Klv3, then Gs is either the induced subgraph (V\ S), or the graph obtained from (V\S) by adding a new vertex adjacent to those x E V\S such that (S U(x