Let 8 be a bipartite graph with edge set β¬and vertex bipartition M, N. The bichromaticity p ( 6) is defined as the maximum number p such that a complete bipartite graph on p vertices is obtainable from 5 by a sequence of identifications of vertices of M or vertices of N. Let p = max{lMI, IN\}. Hara
The bichromaticity of cylinder graphs and torus graphs
β Scribed by Dan Pritikin
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 420 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
The bichromaticity of a bipartite graph B is defined as the maximum value of r + s for which B has the complete bipartite graph K,, as a homomorphic image We determine the bichromaticity of any bipartite cylinder graph C2,, x P, or torus graph CZn x C , , In the process, w e disprove a conjecture of Harary, Hsu, and Miller [Z]
π SIMILAR VOLUMES
We show that if \(G\) is a graph embedded on the torus \(S\) and each nonnullhomotopic closed curve on \(S\) intersects \(G\) at least \(r\) times, then \(G\) contains at least \(\left\lfloor\frac{3}{4} r\right\rfloor\) pairwise disjoint nonnullhomotopic circuits. The factor \(\frac{3}{4}\) is best
## Let be the set of finite, simple and nondirected graphs being not embeddable into the torus. Furthermore let >4 be a partial order-relation and M, (r) the minimal basis of I'. In this paper we determine three graphs of M, (r) being embeddable into the projective plane and containing the subgrap
We show how to construct all the graphs that can be embedded on both the torus and the Klein bottle as their triangulations.