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Quiz 5
MAT 332
Fall 2014
First
Last
Student Number
What is a median ordering?
A median order of a digraph D = (V, A) is a linear order v1 , v2 , . . . , vn of its vertex set V such
that |cfw_(vi , vj ) : i < j| is as large as possible.
Find a median ord
Quiz 9
MAT 332
Fall 2014
First
Last
Student Number
Give a 3-edge colouring of the graph G depicted below:
2
3
1
1
2 1
3
3
3
1 2
3
2
2
1
Let G1 2 be the graph induced by edges that are coloured 1 and 2 and let G1 3 be the graph
induced by edges that are
Quiz 1
First
MAT 332
Fall 2014
Last
Student Number
What is an isomorphism between graphs.
An isomorphism between graphs G and H is a pair of bijections
: V (G) V (H)
and
: E(G) E(H),
so that if an edge e E(G) has end points x, y then the edge (e) E(H)
Quiz 7
First
MAT 332
Fall 2014
Last
Student Number
What is a covering?
A covering K of a graph G a subset of the vertex set of G so that every edge in G has an end
point in K.
In the matching M = cfw_ab, ce, f g, hi below, nd an M augmenting path and us
Quiz 8
First
MAT 332
Fall 2014
Last
Student Number
What is a plane graph?
A plane graph is a graph that can be embedded in the plane.
Show that there may be more than one way to embed a graph in the plane. That is, nd
dierent embedding of a graph G for
Quiz 2
First
MAT 332
Fall 2014
Last
Student Number
What does it mean for a graph to be vertex-transitive?
The graph G = V, E is vertex transitive if for every pair of vertices v, w V , there is an
automorphism of G sending v to w.
Let G be a simple vert
Quiz 4
MAT 332
Fall 2014
First
Last
Student Number
What is a directed Hamilton path?
A directed Hamilton path in a digraph is a spanning subgraph that is isomorphic to a directed
path.
A boss of a tournament is a vertex v from which every vertex is reac
Quiz 3
MAT 332
Fall 2014
First
Last
Student Number
What is a maximal path in a graph G?
A subgraph of G is a maximal path if it is isomorphic to a path and it is not a proper subgraph
any other path in G.
Give an example of a graph G which has two disjo
Exam II
First
MAT 332
Fall 2013
Last
Student Number
To receive full credit you must show all your work. If you run out of room for
an answer, continue on the back of the page.
This exam has 5 questions, for a total of 40 points.
1. (10 points) Dene the fo
Quiz 6
First
MAT 332
Fall 2014
Last
Student Number
For a ow f and in a network N = (D, x, y) and an xpath P , dene (P ).
We dene (P ) to be min
(a) a A(P ) where
(a) =
c(a) f (a) if a is a forward arc of P
f (a)
if a is a reverse arc of P
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Midterm
First
MAT 332
Fall 2013
Last
Student Number
To receive full credit you must show all your work. If you run out of room for
an answer, continue on the back of the page.
This exam has 4 questions, for a total of 40 points.
1. (10 points) Dene the fo