MTH607 (Graph Theory) Course Notes
Lecture 1 January 18, 2016
Example 1.1. The K
onigsberg Bridge Problem. The citizens of Konigsberg (in 1946 the
city was renamed Kaliningrad) wondered whether they could leave home, cross every bridge
exactly once, and r

MTH607 (Graph Theory) Course Notes
Lecture 2 January 25, 2016
Definition 2.1. A subgraph, H, of a graph G, written H G, is a graph such that V (H)
V (G) and E(H) E(G) (clearly, the endpoints of the edges in H must be in V (H).
Example 2.2. In the followi

MTH607 (Graph Theory) Course Notes
Lecture 3 February 1, 2016
Can a bipartite graph have an odd cycle? No. Why not? Turns out, any graph without an
odd cycle is bipartite.
Theorem 3.1. (K
onig, 1936) A graph is bipartite if and only if it has no odd cycle

MTH607 (Graph Theory) Course Notes
Lecture 4 February 8, 2016
Two important principles in discrete mathematics
Now, we are going to discuss two important ideas in discrete mathematics. We will use each
of these to give different proofs of a graph theory s