In this article, we will determine the crossing number of the complete tripartite graphs K,.3.n and K2,3.n. Our proof depends on Kleitman's results for the complete bipartite graphs [D. J. Kleitman, The crossing number of K5,n. J. Combhatorial Theory 9 (1970) 375-3231. a graph G is the minimum numbe
The crossing number ofK3,n in a surface
✍ Scribed by Richter, R. Bruce; ?ir�?, J.
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 174 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0364-9024
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✦ Synopsis
In this article, w e show that the crossing number of K3," in a surface with Euler genus
. This generalizes a result of Guy and Jenkyns, who obtained this result for the torus. 0
📜 SIMILAR VOLUMES
We prove that the crossing number of C5 x C, is 372, which is consistent with the general conjecture that the crossing number of C,, x C, is ( m -2)n, for 3 5 m 5 n.
Let G be a graph on n vertices and m edges. The book crossing number of G is defined as the minimum number of edge crossings when the vertices of G are placed on the spine of a k-page book and edges are drawn on pages, such that each edge is contained by one page. Our main results are t w o polynomi
We introduce a general framework to estimate the crossing number of a graph on a compact 2-manifold in terms of the crossing number of the complete graph of the same size on the same manifold. The bounds are tight within a constant multiplicative factor for many graphs, including hypercubes, some co