## Theorem. A Steinhaus graph is bipartite if and only if it has no triangles. Theorem. If G is a bipartite Steinhaus graph (G ~-~) with partitions X and Y, where Ixl-< IYI, then G has an X-saturated matching.
Characterizations of bipartite Steinhaus graphs
✍ Scribed by Gerard J. Chang; Bhaskar DasGupta; Wayne M. Dymàček; Martin Fürer; Matthew Koerlin; Yueh-Shin Lee; Tom Whaley
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 821 KB
- Volume
- 199
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
We characterize bipartite Steinhaus graphs in three ways by partitioning them into four classes and we describe the color sets for each of these classes. An interesting recursion had previously been given for the number of bipartite Steinhaus graphs and we give two fascinating closed forms for this recursion. Also, we exhibit a lower bound, which is achieved infinitely often, for the number of bipartite Steinhaus graphs.
📜 SIMILAR VOLUMES
Let b(n) be the number of bipartite Steinhaus graphs with n vertices. We show that bin) satisfies the recurrence, b(2)=2, b(3)=4, and for k>~2, b(2k+ 1)=2b(k+ 1)+ 1, b(2k) = b(k) + b(k + 1). Thus b(n) <<, ~zn -~ with equality when n is one more than a power of two. To prove this recurrence, we descr
A signed graph is said to be weakly bipartite if the clutter of its odd circuits is ideal.