A graph H is a cover of a graph G, if there exists a mapping Ο from V (H) onto V (G) such that for every vertex v of G, Ο maps the neighbors of v in H bijectively onto the neighbors of Ο(v) in G. Negami conjectured in 1987 that a connected graph has a finite planar cover if and only if it embeds in
Disjunctive extensions of S4 and a conjecture of Goldblatt's
β Scribed by George F. Schumm
- Publisher
- John Wiley and Sons
- Year
- 1975
- Tongue
- English
- Weight
- 365 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0044-3050
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π SIMILAR VOLUMES
A graph G is k-critical if it has chromatic number k but every proper subgraph of G has a (k&1)-coloring. We prove the following result. If G is a k-critical graph of order n>k 3, then G contains fewer than n&3kΓ5+2 complete subgraphs of order k&1.
We show that conjectures of Thomassen (every 4-connected line graph is hamiltonian) and Fleischner (every cyclically 4-edge-connected cubic graph has either a 3-edge-coloring or a dominating cycle) are equivalent.
We establish an Aomoto-type extension of Askey's last conjectured Selberg q-integral, which was recently proved by Evans. We follow the lines of our proofs of Aomoto-type extensions of the Morris constant term q-identity and Gustafson's Askey-Wilson Selberg q-integral. We require integral forms of t
## Abstract A Short proof is given of the theorem that every grph that does not have __K__~4~ as a subcontraction is properly vertex 3βcolorable.