The graphs below have chromatic numbers 5 and 2. G is a set C of G's nodes such each pair of nodes in C is connected by an edge. If a clique has k nodes it is called a k-clique . The size of the largest clique in a graph is said to be the clique number of the graph. It is easy to see that the clique number of K n is n.
G is a path that includes each node of G exactly once.
A Hamiltonian graph is a one with a Hamiltonian circuit. Show that every complete graph is a Hamiltonian graph. If the first and last nodes of an Euler path are the same it is said to be an Euler circuit . In the city of Koenigsberg there are two islands in a river and 7 bridges. Restate this problem as a graph problem.