| EPSRC Reference: |
GR/R01217/01 |
| Title: |
Uniqueness of 2-Factors |
| Principal Investigator: |
Sheehan, Dr J |
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| Department: |
Mathematical Sciences |
| Organisation: |
University of Aberdeen |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
15 July 2001 |
Ends: |
14 January 2002 |
Value (£): |
8,200
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Summary on Grant Application Form |
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Let H(k) be the set of finite, k-regular k-edge connected Hamiltonian graphs such that their only 2-factors are Hamiltonian cycles. For example the Heawood graph belongs to H(3). Using recent results of (Robertson, Seymour, Thomas and McCuaig 1999) it is hoped to obtain a characterisation of the elements of BH(3) (where B adds the condition of bipartity) in terms of iterated products of the Heawood graph.We conjecture that H(4) contains very few exceptional graphs. To prove this our approach is:(i) using the structure of BH(3) show that BH(4) consists of a few exceptional graphs;(ii) to prove that any element of H(4) contains an element of BH(4);(iii) in order to prove (ii) develop a reduction technique which describes how sets of edges can be extended to 2-factors.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.abdn.ac.uk |