Abstract:Label the vertices of the complete graph K v with the integers {0, 1, . . . , v − 1} and define the length of the edge between x and y to be min(|x − y|, v − |x − y|). Let L be a multiset of size v − 1 with underlying set contained in {1, . . . , v/2 }. The Buratti-Horak-Rosa Conjecture is that there is a Hamiltonian path in K v whose edge lengths are exactly L if and only if for any divisor d of v the number of multiples of d appearing in L is at most v − d.We introduce "growable realizations," which enable u… Show more
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