Crystallographic nets and their quotient graphs
β Scribed by W. E. Klee
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 151 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0232-1300
No coin nor oath required. For personal study only.
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## Abstract Let __G__ be an infinite 4βconnected planar graph such that the deletion of any finite set of vertices from __G__ results in exactly one infinite component. Dean __et al__. proved that either __G__ admits a radial net or a special subgraph of __G__ admits a ladder net, and they used the
## Abstract A graph is __kβindivisible__, where __k__ is a positive integer, if the deletion of any finite set of vertices results in at most __k__ β 1 infinite components. In 1971, NashβWilliams conjectured that a 4βconnected infinite planar graph contains a spanning 2βway infinite path if and onl