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Knots in Hamilton Cycles

✍ Scribed by Mansfield, Marc L.


Book ID
126876347
Publisher
American Chemical Society
Year
1994
Tongue
English
Weight
376 KB
Volume
27
Category
Article
ISSN
0024-9297

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πŸ“œ SIMILAR VOLUMES


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✍ TomΓ‘Ε‘ Kaiser; ZdenΔ›k RyjÑček; Daniel KrΓ‘l; Moshe Rosenfeld; Heinz-JΓΌrgen Voss πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 300 KB

## Abstract The prism over a graph __G__ is the Cartesian product __G__ β–‘ __K__~2~ of __G__ with the complete graph __K__~2~. If __G__ is hamiltonian, then __G__β–‘__K__~2~ is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxati

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The edges of the complete graph K, are coloured so that no colour appears more than k = k(n) times, k=rn/(A In n)l, for some sufficiently large A. We show that there is always a Hamiltonian cycle in which each edge is a different colour. The proof technique is probabilistic.

Oriented hamilton cycles in digraphs
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## Abstract We show that a directed graph of order __n__ will contain __n__‐cycles of every orientation, provided each vertex has indegree and outdegree at least (1/2 + __n__^‐1/6^)__n__ and __n__ is sufficiently large. Β© 1995 John Wiley & Sons, Inc.

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## Abstract We extend Whitney's Theorem that every plane triangulation without separating triangles is hamiltonian by allowing some separating triangles. More precisely, we define a decomposition of a plane triangulation __G__ into 4‐connected β€˜pieces,’ and show that if each piece shares a triangle

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## UNIVERSIW OF WATERLOO ' The research reported here has been sponsored by the Canadian Commonwealth Association.