Bang For Your Buck Hd Camcorder

EXTRA POINTS PROJECT Project 5 4

Hamilton Highway

In the mathematical field of graph theory, a Hamiltonian path in a graph is a path , a succession of adjacent edges, which visits all vertices of the graph once. If also the last vertex visited is adjacent to p irst, the path is a Hamiltonian cycle .
The problem of finding a cycle (or path) Hamiltonian an arbitrary graph is known to NP-complete .
The Hamiltonian paths and cycles were named after William Rowan Hamilton , inventor of the game Hamilton, threw a toy that involves finding a Hamiltonian cycle on the edges of a graph of a dodecahedron . Hamilton solved this problem by using quaternions , but this solution does not generalize to all graphs.

A Hamiltonian path is a path that visits each vertex exactly once. A graph containing a Hamiltonian path is called a Hamiltonian cycle or circuit Hamiltonian if it is a cycle that visits each vertex exactly once (except the apex of which party and which arrives). A graph containing a Hamiltonian cycle graph is called Hamiltonian .
can also say that Hamiltonian graphs are when they meet:
-Hamiltonian Circuit -must be related, must be closed.

to summarize: hamilton Road is a walkway that goes all the edges only 1 time, arriving at the same point.

Exercise:
there is a problem for such famous examples:

a chess board try to make that horse, scroll all the board squares

Neither algorithm guarantees an optimal solution. However, usually both are good solutions, close to the optimal.

THEOREM: Let K

* n a complete directed graph, ie K * n is nv 'erotic
and for any pair of v' erotic different x, and at least the edge (x, y) or (y, x)
est 'to K * n. This graph always contains a Hamilton path .

PROOF:

Let m ≥ 2 with Tm a simple path that contains the m-1 edges (v1, v2), (v2, v3 ),...,( vm -1, vm). If m = n is finished, otherwise v is a v 'erotic does not appear in tm.

If (v, v1) is an edge of K * n can be extended tm adding this edge. In another case
(v1, v) should be an edge. Suppose now that (v, v2) is in the graph. Then there is the greatest path (v1, v), (v, v2), (v2, v3 ),...,( vm-1, vm).

If (v, v2) is not an edge K * n then (v2, v) should be . According

continues this process there are only two possibilities :

1. for 1 ≤ k ≤ m-1 edges ( vk, v), (v, vk +1) are replaced K * n ( vk, vk +1) for this pair of edges

2. ( vm, v) is in K * n and adds this edge to tm.

In any case, we obtain results in a simple way tm including m +1 +1 has m vertices and edges. This process can be repeated until there is a path of n vertices.

BIBLIOGRAPHY :
http://es.wikipedia.org/wiki/Camino_hamiltoniano
http://docs.google.com/viewer?a=v&q=cache:JNDPlNjUeggJ:www.matap.uma.es/profesor/magalan/MatDis/material/GrafosTema5_1_MatDiscreta.pdf+caminos+de+hamilton& hl =es& gl = mx & pid = bl & srcid = ADGEESjhF 5 pcBVaMbrj 8 kWCfuPdH 4 CVND 5 lKIyifHirJg 6 Wi 48 mGQJPdZAnrvC 3y5 aU 6 zwOJstFridndiLhVsNnEZmHNiT 4 Dq 8 eyp 4 XnqA 6 tEjWcK 9 wj 3 hffTsTdMiynAwAKVx 1 boWKm & sig = AHIEtbTAHM 1- WypcKHRi 25 gFE 92 alt 3 ofQ
http://docs.google.com/viewer?a=v&q=cache:7CjbQrO-eUIJ:www.fing.edu.uy/tecnoinf/cursos/mdl2/material/teo/teorico2.pdf+caminos+de+hamilton& hl =es& gl = mx & pid = bl & srcid = ADGEESgw 7 LRDpcJCpSyzGyrAJuGasfz 72 trbe 0_ DB 6 And _ CA 9o- tIqipWnMUho - aEnjfg 5C0 ev 4 FPU 3B2 OvQJ __ szzb 8 ICDE -K4e- QOxk - idphdOji 1T_ hOiEzTHd 9 USgf 8 ysHBTyDU 7s & themselves = AHIEtbRANt 1P1 qlH 2C9 kBAV 0A2 ck 182 FTA