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The Hamiltonian Circuit Algorithm
Ashay Dharwadker
The Hamiltonian Circuit Algorithm
Ashay Dharwadker
We present a new polynomial-time algorithm for finding Hamiltonian circuits in graphs. It is shown that the algorithm always finds a Hamiltonian circuit in graphs that have at least three vertices and minimum degree at least half the total number of vertices. In the process, we also obtain a constructive proof of Dirac?s famous theorem of 1952, for the first time. The algorithm finds a Hamiltonian circuit (respectively, tour) in all known examples of graphs that have a Hamiltonian circuit (respectively, tour). In view of the importance of the P versus NP question, we ask: does there exist a graph that has a Hamiltonian circuit (respectively, tour) but for which this algorithm cannot find a Hamiltonian circuit (respectively, tour)? The algorithm is implemented in C++ and the program is demonstrated with several examples.
Media | Boeken Paperback Book (Boek met zachte kaft en gelijmde rug) |
Vrijgegeven | 2 oktober 2011 |
ISBN13 | 9781466381377 |
Uitgevers | CreateSpace Independent Publishing Platf |
Pagina's | 32 |
Afmetingen | 2 × 216 × 279 mm · 104 g |
Taal en grammatica | Engels |