v
u
w
Figure 1: Counterexample for Problem 1a).
MATH 350: Graph Theory and Combinatorics. Fall 2014.
Assignment #1: Paths, Cycles and Trees. Solutions.
1.
For each of the following statements decide if it is true or false, and
either prove it or give a co
MATH 350: Graph Theory and Combinatorics. Fall 2014.
Assignment #5: Planar graphs. Solutions.
1.
A graph G is outerplanar if it can be drawn in the plane so that
every vertex is incident with the innite region. Show that a graph G is
outerplanar if and on
MATH 350: Graph Theory and Combinatorics. Fall 2014.
Assignment #4: Ramsey theorem, matching and vertex coloring. Solutions.
1.
Show that R(3, 4) = 9.
Solution: First we show that R(3, 4) 9. Let G be a graph with |V (G)| = 9. Our goal
is to show that (G)
MATH 350: Graph Theory and Combinatorics. Fall 2014.
Assignment #3: Mengers theorem, vertex covers and network ows.
1.
Show that (G) 1 (|E(G)| + 1) for every connected graph G.
2
Solution: By induction on |V (G)|. Base case for |V (G)| 2 is routine.
Induc
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