The projective plane crossing numbers of circular graphs*
✍ Scribed by Dengju MA; Han REN
- Book ID
- 107347074
- Publisher
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences
- Year
- 2008
- Tongue
- English
- Weight
- 486 KB
- Volume
- 21
- Category
- Article
- ISSN
- 1009-6124
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 _
## Abstract In this paper, we show that the projective plane crossing number of the graphs __C__~3~ × __C__~__n__~ is __n__ ‐ 1 for __n__ ≤ 5 and 2 for __n__ = 4. As far as we can tell from the literature, this is the first infinite family of graphs whose crossing number is known on a single surfac