A graph G is an apex graph if it contains a vertex w such that G&w is a planar graph. It is easy to see that the genus g(G) of the apex graph G is bounded above by {&1, where { is the minimum face cover of the neighbors of w, taken over all planar embeddings of G&w. The main result of this paper is
The Genus Problem for Cubic Graphs
β Scribed by Carsten Thomassen
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 206 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
We prove that the following problem is NP-complete: Given a cubic graph G and a natural number g, is it possible to draw G on the sphere with g handles added?
π SIMILAR VOLUMES
In this short paper, we give a positive answer to a question of C. D. Godsil (1983, Europ. J. Combin. 4, 25 32) regarding automorphisms of cubic Cayley graphs of 2-groups: ``If Cay(G, S) is a cubic Cayley graph of a 2-group G and A=Aut Cay(G, S), does A 1 {1 imply Aut(G, S){1?'' 1998 Academic Press
## Abstract Every 3βconnected planar, cubic, triangleβfree graph with __n__ vertices has a bipartite subgraph with at least 29__n__/24βββ7/6 edges. The constant 29/24 improves the previously best known constant 6/5 which was considered best possible because of the graph of the dodecahedron. Example
It is shown that there exists a decomposition of K,, into edge-disjoint copies of the Petersen graph if and only if 'u = 1 or 10 (mod 151, 'u # 10.