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MGF 1107 – EXPLORATIONS IN MATHEMATICS
LECTURE 16
Hamilton Paths and Hamilton Circuits
Before formally defining Hamilton paths and Hamilton circuits, consider
the example below.
Ex.
The following table lists the least expensive oneway fares offered
between four cities.
Orlando
Atlanta
Memphis
New Orleans
Orlando (O)
*
Atlanta (A)
*
Memphis (M)
*
New Orleans (N)
*
We can create a graph to illustrate this information, letting the vertices
represent the cities and listing the airfares on the corresponding edges.
It should be noted that the cost of the oneway flight does not depend on
the city of origin. So a flight from Orlando to Atlanta costs the same as
one from Atlanta to Orlando. This allows us to list the prices on the
edges. We call such graphs weighted graphs
.
The typical problem we look at concerns finding the minimum cost of
flying to each of the cities involved before flying back to the original
departure point. We call them traveling salesman problems
.
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 Spring '08
 EVINSON
 Math, Calculus

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