Hamiltonian circuits
- To: mathgroup at smc.vnet.net
- Subject: [mg67878] Hamiltonian circuits
- From: Frank Brand <frank.brand at t-online.de>
- Date: Tue, 11 Jul 2006 05:58:54 -0400 (EDT)
- References: <e8lfpl$r18$1@smc.vnet.net> <e8nt8i$k81$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Dear Zhu Guohun , Dear Leigh, thanks for your postings. Indeed I made a mistake concerning my adjacency matrix. The correct one is AdjMatrix = {{0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}} So, in my special field of interest I also treat {1, 2, 1} as a circuit allthough in the literature the mathematical definition needs at least three vertices. In the case of the above adjacency matrix there are the following list of all possible circuits on all subgraphs of the original graph. AllCircuits= {{1, 2, 1}, {5, 19, 5}, {13, 14, 13}, {1, 3, 2, 1}, {6, 13, 14, 6}, {6, 20, 21, 6}, {1, 11, 18, 8, 1}, {2, 6, 19, 5, 2}, {8, 17, 19, 18, 8}, {1, 11, 18, 9, 2, 1}, {2, 6, 19, 18, 9, 2}, {1, 2, 6, 19, 18, 8, 1}, {1, 3, 15, 11, 18, 8, 1}, {1, 11, 18, 8, 9, 2, 1}, {2, 6, 13, 12, 18, 9, 2}, {2, 6, 16, 11, 18, 9, 2}, {2, 6, 19, 18, 8, 9, 2}, {2, 6, 20, 12, 18, 9, 2}, {5, 19, 18, 8, 17, 10, 5}, {8, 17, 10, 15, 11, 18, 8}, { 1, 2, 6, 13, 12, 18, 8, 1}, {1, 2, 6, 16, 11, 18, 8, 1}, {1, 2, 6, 20, 12, 18, 8, 1}, {1, 3, 2, 6, 19, 18, 8, 1}, {1, 3, 15, 11, 18, 9, 2, 1}, {2, 6, 13, 12, 18, 8, 9, 2}, {2, 6, 13, 16, 11, 18, 9, 2}, {2, 6, 16, 11, 18, 8, 9, 2}, {2, 6, 20, 12, 18, 8, 9, 2}, {2, 6, 20, 16, 11, 18, 9, 2}, {5, 16, 11, 18, 8, 17, 10, 5}, {5, 16, 11, 18, 8, 17, 19, 5}, {6, 19, 18, 8, 17, 10, 21, 6}, { 1, 2, 6, 13, 16, 11, 18, 8, 1}, {1, 2, 6, 20, 16, 11, 18, 8, 1}, {1, 3, 2, 6, 13, 12, 18, 8, 1}, {1, 3, 2, 6, 16, 11, 18, 8, 1}, {1, 3, 2, 6, 20, 12, 18, 8, 1}, {1, 3, 15, 11, 18, 8, 9, 2, 1}, {1, 11, 18, 8, 17, 10, 5, 2, 1}, {1, 11, 18, 8, 17, 19, 5, 2, 1}, {2, 6, 13, 12, 16, 11, 18, 9, 2}, {2, 6, 13, 16, 11, 18, 8, 9, 2}, {2, 6, 19, 5, 16, 11, 18, 9, 2}, {2, 6, 19, 18, 8, 17, 10, 5, 2}, {2, 6, 20, 12, 16, 11, 18, 9, 2}, {2, 6, 20, 16, 11, 18, 8, 9, 2}, {6, 13, 12, 18, 8, 17, 10, 21, 6}, {6, 16, 11, 18, 8, 17, 10, 21, 6}, {6, 20, 12, 18, 8, 17, 10, 21, 6}, {1, 2, 6, 13, 12, 16, 11, 18, 8, 1}, {1, 2, 6, 19, 5, 16, 11, 18, 8, 1}, {1, 2, 6, 20, 12, 16, 11, 18, 8, 1}, {1, 3, 2, 6, 13, 16, 11, 18, 8, 1}, {1, 3, 2, 6, 20, 16, 11, 18, 8, 1}, {2, 6, 13, 12, 16, 11, 18, 8, 9, 2}, {2, 6, 13, 12, 18, 8, 17, 10, 5, 2}, {2, 6, 13, 12, 18, 8, 17, 19, 5, 2}, {2, 6, 16, 11, 18, 8, 17, 10, 5, 2}, {2, 6, 16, 11, 18, 8, 17, 19, 5, 2}, {2, 6, 19, 5, 16, 11, 18, 8, 9, 2}, {2, 6, 20, 12, 16, 11, 18, 8, 9, 2}, {2, 6, 20, 12, 18, 8, 17, 10, 5, 2}, {2, 6, 20, 12, 18, 8, 17, 19, 5, 2}, {6, 13, 16, 11, 18, 8, 17, 10, 21, 6}, {6, 20, 16, 11, 18, 8, 17, 10, 21, 6}, {1, 3, 2, 6, 13, 12, 16, 11, 18, 8, 1}, {1, 3, 2, 6, 19, 5, 16, 11, 18, 8, 1}, {1, 3, 2, 6, 20, 12, 16, 11, 18, 8, 1}, { 1, 3, 15, 11, 18, 8, 17, 10, 5, 2, 1}, {1, 3, 15, 11, 18, 8, 17, 19, 5, 2, 1}, {2, 6, 13, 16, 11, 18, 8, 17, 10, 5, 2}, {2, 6, 13, 16, 11, 18, 8, 17, 19, 5, 2}, {2, 6, 20, 16, 11, 18, 8, 17, 10, 5, 2}, {2, 6, 20, 16, 11, 18, 8, 17, 19, 5, 2}, {5, 16, 11, 18, 8, 17, 10, 21, 6, 19, 5}, {6, 13, 12, 16, 11, 18, 8, 17, 10, 21, 6}, {6, 20, 12, 16, 11, 18, 8, 17, 10, 21, 6}, {1, 11, 18, 8, 17, 10, 21, 6, 19, 5, 2, 1}, {2, 6, 13, 12, 16, 11, 18, 8, 17, 10, 5, 2}, {2, 6, 13, 12, 16, 11, 18, 8, 17, 19, 5, 2}, {2, 6, 20, 12, 16, 11, 18, 8, 17, 10, 5, 2}, {2, 6, 20, 12, 16, 11, 18, 8, 17, 19, 5, 2}, {1, 3, 15, 11, 18, 8, 17, 10, 21, 6, 19, 5, 2, 1}} I read very carefully the entire documentation of the combinatorica package but it seems that there is no procedure with a good time behaviour to detect all subgraphs containing Hamiltonian cycles? Any help or hints are very welcome. Greetings Frank