CS180 Winter 2011
Homework 3
The following homework is due Wednesday, January 26 at the beginning of lecture.
When submitting your homework, please include your name at the top of each page. If you submit
multiple pages, please staple them together. We also ask that you do something to indicate which
name is your last name on the ﬁrst page, such as underlining it.
Please provide complete arguments and time complexity analysis for all solutions,
unless otherwise stated.
1. Given a graph
G
, the
Line Graph
G
0
of
G
is a graph where all edges in
G
are vertices in
G
0
. Two vertices in
G
0
(which were edges in
G
) have an edge between them iﬀ their edges in
G
are both incident to a common vertex.
Prove or disprove: The line graph of a bipartite graph is a bipartite graph.
2. For an undirected connected graph
G
= (
V,E
), an
Euler
1
Tour
is an ordering
t
1
,t
2
,...t
m
of edges such that any two consecutive edges in the ordering share a vertex and each edge
appears once in the ordering. That is, it is a path that travels across each
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 Spring '08
 MOLOUDI
 Graph Theory, line graph, Glossary of graph theory, Eulerian path, Bipartite graph

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