On 3-Transitive Graphs of Girth 6
β Scribed by K. Ching
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 313 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
We prove that every planar graph of girth at least 5 is 3-choosable. It is even possible to precolor any 5-cycle in the graph. This extension implies GrΓΆtzsch's theorem that every planar graph of girth at least 4 is 3-colorable. If 1995 Academic Press, Inc.
A graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circumference. In answer to a question of ErdΕs, we show that a Hamiltonian weakly-pancyclic graph of order n can have girth as large as about 2 n/ log n. In contrast to this, we show that the existence of
## Abstract With the aid of a computer. we give a regular graph of girth 6 and valency 7, which has 90 vertices and show that this is the unique smallest graph with these properties.
We examine the existing constructions of the smallest known vertex-transitive graphs of a given degree and girth 6. It turns out that most of these graphs can be described in terms of regular lifts of suitable quotient graphs. A further outcome of our analysis is a precise identification of which of
Let G be a regular graph of girth n( 2 5 ) and valency k ( r 3 ) , that has the least possible number f(k, n ) of vertices. Although the existence of such a graph was proved by Erdos and Sachs (see Ref. 6, p. 82), only a few cases have been solved (see Refs. 2-7). Recently, O'Keefe and Wong have sho