Math 103, Spring 2011, Solutions to Chapter 5 Homework Set
Problem 20:
Comment:
Each block which has houses on both sides of the street is represented by a pair of edges
(since the mail carrier must make two passes on such blocks). Each block which has houses on only
one side of the street is represented by a single edge.
Note that the mail carrier has no need to walk along the outer edge of the park, where no houses are
located, so our graph contains no edges representing such streets.
In this way, the graph contains all the
information relevant to the mail carrier's task, and only such information.
Problem 26:
(a)
The graph has an Euler path, since the graph is connected and has exactly two odd vertices.
Note
that since the graph has an Euler path, it does not have an Euler circuit.
(b)
The graph has an Euler circuit, since the graph is connected and has no odd vertices at all.
Note
that since the graph has an Euler circuit, it does not have an Euler path.
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 Spring '07
 Berkowitz
 Math, Graph Theory, Vertex, Leonhard Euler, Graph theory objects, Seven Bridges of Königsberg

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