Pairs of Adjacent Hamiltonian Circuits with Small Intersection | Zendy

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Pairs of Adjacent Hamiltonian Circuits with Small Intersection

Author(s) -

West Douglas B.

Publication year - 1978

Publication title -

studies in applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 46

eISSN - 1467-9590

pISSN - 0022-2526

DOI - 10.1002/sapm1978593245

Subject(s) - hamiltonian (control theory) , mathematics , electronic circuit , polytope , combinatorics , hamiltonian path , intersection (aeronautics) , regular polygon , connection (principal bundle) , travelling salesman problem , discrete mathematics , topology (electrical circuits) , geometry , algorithm , graph , physics , mathematical optimization , quantum mechanics , engineering , aerospace engineering

Consider the question: When can the edges in a pair of Hamiltonian circuits be redistributed to form another pair of circuits with the same union and intersection? A class of pairs is exhibited which intersect in two edges and cannot be rearranged in this way. A connection to algorithms for the traveling salesman problem is explained using the convex polytope of Hamiltonian circuits in . The exhibited pair is shown to be an edge of that polytope.

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