MATH 239 Assignment 5
This assignment is due at noon on Friday, July 10, 2009, in the drop boxes opposite the
Tutorial Centre, MC 4067.
Note:
The notation
e
=
uv
is a shorthand for
e
=
{
u,v
}
. Even though we use the
shorthand here, it is always understood that an edge is a subset of the vertices of size 2.
1. For each of the following descriptions of possible graphs, either show that one
exists by drawing an example, or prove that such a graph does not exist.
(a) A 3regular graph that contains a bridge.
(b) A 4regular graph that contains a bridge.
(c) A graph whose minimum degree is 4 (i.e. every vertex has degree at least 4)
that contains a bridge.
2. Determine the minimum number of vertices
r
in any tree
T
having two vertices
of degree 3, two vertices of degree 4, and one vertex of degree 6. Show that your
answer is best possible by giving an example of such a tree with exactly
r
vertices.
3. Let
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 M.PEI
 Math, Combinatorics, Graph Theory, vertices, Tutorial Centre

Click to edit the document details