On polynomials and crossing numbers of complete graphs
✍ Scribed by Thomas L Saaty
- Publisher
- Elsevier Science
- Year
- 1971
- Tongue
- English
- Weight
- 77 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract The __crossing number__, cr(__G__), of a graph __G__ is the least number of crossing points in any drawing of __G__ in the plane. According to the Crossing Lemma of M. Ajtai, V. Chvátal, M. Newborn, E. Szemerédi, Theory and Practice of Combinatorics, North‐Holland, Amsterdam, New York,
## Abstract Crossing numbers of Sierpiński graphs __S__(__n__,__k__) and their regularizations __S__^+^(__n__,__k__) and __S__^++^(__n__,__k__) are studied. Drawings of these graphs are presented and proved to be optimal for __S__^+^(__n__,__k__) and __S__^++^(__n__,__k__) for every __n__ ≥ 1 and _
In his paper on the crossing numbers of generalized Petersen graphs, Fiorini proves that P(8, 3) has crossing number 4 and claims at the end that P(10, 3) also has crossing number 4. In this article, we give a short proof of the first claim and show that the second claim is false. The techniques are