On the Crossing Number of Complete Graphs
β Scribed by O. Aichholzer; F. Aurenhammer; H. Krasser
- Publisher
- Springer Vienna
- Year
- 2005
- Tongue
- English
- Weight
- 135 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0010-485X
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π SIMILAR VOLUMES
## Abstract Necessary and sufficient conditions are given for a nonplanar graph to have a line graph with crossing number one. This corrects some errors in Kulli et al. 4. Β© 2001 John Wiley & Sons, Inc. J Graph Theory 37: 181β188, 2001
## Abstract We prove that for every prime number __p__ and odd __m__>1, as __s__ββ, there are at least __w__ face 2βcolorable triangular embeddings of __K__~__w, w, w__~, where __w__ = __m__Β·__p__^__s__^. For both orientable and nonorientable embeddings, this result implies that for infinitely many
## Abstract In this paper we deduce a necessary and sufficient condition for a line grah to have crossing number 1. In addition, we prove that the line graph of any nonplanar graph has crossing number greater than 2.