Interchange graphs and the Hamiltonian cycle polytope
β Scribed by Gerard Sierksma
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 464 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0166-218X
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β¦ Synopsis
This paper answers the (non)adjacency question for the whole spectrum of Hamiltonian cycles on the Hamiltonian cycle polytope (HC-polytope), also called the symmetric traveling salesman polytope, namely from Hamiltonian cycles that differ in only two edges through Hamiltonian cycles that are edge disjoint. The HC-polytope is the convex hull of the characteristic vectors
π SIMILAR VOLUMES
denote the set of all m Γ n {0, 1}-matrices with row sum vector R and column sum vector S. Suppose A(R, S) ] ". The interchange graph G(R, S) of A(R, S) was defined by Brualdi in 1980. It is the graph with all matrices in A(R, S) as its vertices and two matrices are adjacent provided they differ by
We prove that there exists a cyclic Hamiltonian k-cycle system of the complete graph if and only if k is odd but k = 15 and p with p prime and ΒΏ 1. As a consequence we have the existence of a cyclic k-cycle system of the complete graph on km vertices for any pair (k; m) of odd integers with k as abo