This paper shows that a simple graph which can be cellularly embedded on some closed surface in such a way that the size of each face does not exceed 7 is upper embeddable. This settles one of two conjectures posed by Nedela and S8 koviera (1990, in ``Topics in Combinatorics and Graph Theory,'' pp.
The Relative Maximum Genus of a Graph
โ Scribed by C.P. Bonnington
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 422 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investiga
## Abstract The cochromatic number of a graph __G__, denoted by __z__(__G__), is the minimum number of subsets into which the vertex set of __G__ can be partitioned so that each sbuset induces an empty or a complete subgraph of __G__. In this paper we introduce the problem of determining for a surf
## Abstract Examples are given to show that the nonorientable genus of a graph is not additive over its blocks. A nonorientable analog for the Battle, Harary, Kodama, and Youngs Theorem is proved; this completely determines the nonorientable genus of a graph in terms of its blocks. It is also shown