1. Exam 3 review
Chapter 9- Graphs

2. Basics and proofs to know well
Special graphs: Kn, Cn, Wn, Qn, Km,n
Use these for calculations, counterexamples…
Know the definitions of bipartite, isomorphic, and planar
Prove:
Bipartite
or not
Isomorphic
Planar
Euler circuit or path possible
Other proofs– be able to supply some details, as we do in class on harder problems

3. Theorems to know for the unit test
9.2: Thm. 1 Handshaking: 2e= sum of deg(v)
Thm. 2: undirected graph has an even # of odd degree
Conditions for when an Euler path or circuit exist (don’t worry about Hamilton conditions)
9.7: Euler: r=e-v+2
Cor 1: connected, planar, simple, e≤ ev-6
Cor 3: no circuits length 3, then e≤2v-4
Thm. 2: A graph is nonplanar iff it contains a subgraph homeomorphic to K3,3 or K5.
9.8: Thm 1- chromatic # of planar graph ≤4

4. Calculations to do Calculate deg, deg-, deg+
Adjacency tables and matrices
Paths
Strong and weakly connected
Counting paths of a certain length l
Euler and Hamilton paths and circuits
Conditions for Euler paths and circuits (not for Hamilton)
Chromatic number of special graphs