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Handout 5.3 Graph Coloring
Peer instruction questions 1–3.
Let \(\bfG=(V,E)\) be a graph. Then \(\phi\colon V\to C\) is a proper coloring of \(\bfG\) if
\(xy\in E\) implies
\(\phi(x)\neq \phi(y)\)
\(\phi\) uses as few colors from
\(C\) as possible
Let \(\bfG=(V,E)\) be a graph and \(\phi\colon V\to C\) be a proper coloring of \(\bfG\text{.}\) Let \(S\) be all vertices colored \(1\in C\text{.}\) How many edges does the subgraph of \(\bfG\) induced by \(S\) contain?
What is the chromatic number of the complete graph on \(n\) vertices \(\bfK_{n}\text{?}\)
There is no fixed formula depending on
\(n\text{.}\)
Definition 5.9 .
A graph is
bipartite provided that its chromatic number is
\(2\text{.}\)
Theorem 5.10 .
A graph is bipartite if and only if it does not contain any odd cycles.
Peer instruction question 4.
