The Hamiltonian Circuit Algorithm (Paperback) (ISBN-13: 9781466381377)

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.

Author: Ashay Dharwadker
ISBN-10: 146638137X
ISBN-13: 9781466381377
Publisher: Createspace Independent Publishing Platform
Language: English
Published: 10/02/2011
Pages: 34
Format: Paperback
Weight: 0.23lbs
Size: 11.00h x 8.50w x 0.09d