The University of Sydney
School of Mathematics and Statistics
Solutions to Quiz 2
MATH2069/2969: Discrete Mathematics and Graph Theory
Semester 1, 2009
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MATH2069
MATH2969
This quiz lasts 30 minutes. There are a total of 30 marks. Note that the true/false parts
of question 7 are worth half a mark each.
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1.
Complete the following definitions.
(a)
If
v
and
w
are vertices of a graph
G
, we say that
v
is linked to
w
in
G
if
there is a walk from
v
to
w
in
G
.
(b)
If
v
is a vertex of a graph
G
, the degree deg(
v
) is
the number of edges ending at
v
.
(c)
A connected graph with
≥
3 vertices is Hamiltonian if it has a walk which
returns to its starting vertex and
visits every vertex exactly once.
(d)
In a connected weighted graph, the Chinese Postman Problem is to find a
walk which has minimal weight subject to the following constraints: it must
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 Spring '09
 Math, Statistics, Graph Theory, Travelling salesman problem, Chinese Postman Problem, University of Sydney School of Mathematics, Graph Theory Semester

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