Abstract
Abstract In this paper, we consider the problem of searching for undirected Hamiltonian circuits in the complete graph on n vertices with the use of unconditional edge tests. We prove that the minimal test contains exactly n(n - 3)/2 - [n/3] + 1 edges. We propose an explicit characterisation of all minimal difference sets of edges. This research was supported by the Russian Foundation for Basic Research, grants 02-01-00985 and 00-15-96103, by the Program ‘Universities of Russia,’ and the Federal Program ‘Integration.’
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