Hamilton Paths and Hamilton Circuits
Unit 3Thinking mathematically by BlitzerHamilton Paths and
Hamilton CircuitsWe have studied paths and circuits that covered
every edge of a graph. Using every edge of a graph is helpful for
garbage collection, curb sweeping , or snow removal.
What about a UPS driver trying to find the best way to deliver
packages around town?
In this situation a driver is only concerned about finding a
path that passes through each vertex of the graph only once. Thus,
it is not important to use every road or edge between the delivery
locations. Thinking mathematically by Blitzer Pg: 842Hamilton PathA
path that passes all the vertices of a graph exactly once (must
include all vertices).
Hamilton CircuitStarts at a vertex and visits each vertex once
and only once, returning to where it started.
The number of Hamilton circuits in a complete graphIf you have a
graph that is complete and has a Hamilton circuit it has multiple
sequences that will produce the same Hamilton circuit.
In order to avoid a duplication you can start and end at vertex
A.How many unique Circuits can you get from a complete Hamilton
graph with four vertices? ABCDThe number of Hamilton circuits in a
complete graphThe number of Hamilton circuits in a complete graph
with n vertices.(n-1)!
Determine the number of Hamilton circuits in a complete graph
with:Four verticesFive VerticesEight Vertices Weighted GraphIs when
we assign numbers to the edges of a graph.
