ICS 163 - Graph Algorithms Homework 6, 50 Points
Due: Wednesday, March 12, 2003
Use Kuratowski's Theorem to
prove that the following graph, called Petersen's graph, is
Show how to draw each of the following graphs
on the surface of a torus (i.e., a "donut" with a hole in the middle)
so that no two two edges cross.
Draw a biconnected planar graph G
with 10 vertices that has a separating cycle C with 6 vertices
such that there are 5 pieces with respect to C that induce an
interlacement graph with 6 edges.
Give an example of a biconnected graph G and a separating cycle
C in G such that the interlacement graph for the pieces of
G with respect to C has
at least cn2 edges, for some constant c > 0.
Let P be a piece of a biconnected graph with respect to a
- Show that if P
has at least one vertex, the number of edges of P is great
than or equal to the number of attachments of P.
- Show that the graph obtained by adding P to C is