EPSRC Reference: 
GR/R01217/01 
Title: 
Uniqueness of 2Factors 
Principal Investigator: 
Sheehan, Dr J 
Other Investigators: 

Researcher CoInvestigators: 

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Department: 
Mathematical Sciences 
Organisation: 
University of Aberdeen 
Scheme: 
Standard Research (PreFEC) 
Starts: 
15 July 2001 
Ends: 
14 January 2002 
Value (£): 
8,200

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Summary on Grant Application Form 
Let H(k) be the set of finite, kregular kedge connected Hamiltonian graphs such that their only 2factors 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 2factors.

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