Knots and Graphs I—Arc Graphs and Colorings
✍ Scribed by Frank Harary; Louis H. Kauffman
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 451 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0196-8858
No coin nor oath required. For personal study only.
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## Abstract The main purpose of this paper is to show that any embedding of __K~7~__ in three‐dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of __K~6~__ contains a pair of disjoint cycles which are homologically linked.
## Abstract We show that for an interval graph given in the form of a family of intervals, a maximum independent set, a minimum covering by disjoint completely connected sets or cliques, and a maximum clique can all be found in __O__(__n__ log __n__) time [__O__(__n__) time if the endpoints of the