On Hamiltonian Regular Graphs of Girth Six
β Scribed by Brown, W. G.
- Book ID
- 120098730
- Publisher
- Oxford University Press
- Year
- 1967
- Tongue
- English
- Weight
- 183 KB
- Volume
- s1-42
- Category
- Article
- ISSN
- 0024-6107
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π SIMILAR VOLUMES
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
In this paper it is shown that any rn-regular graph of order 2rn (rn 3 3), not isomorphic to K, , , , or of order 2rn + 1 (rn even, rn 3 4), is Hamiltonian connected, which extends a previous result of Nash-Williams. As a corollary, it is derived that any such graph contains at least rn Hamiltonian
We construct a graph of girth 6 that cannot be oriented as the diagram of an ordered set and discuss the reasons why this particular construction cannot be extended to produce examples of larger girth. The problem of characterizing graphs that can be oriented as diagrams of ordered sets (or coverin