Computing cliques, lecture 5/6/04
Homework due 5/13/04

Let chi(G) denote the chromatic number of the graph G and
cl(G) be the order (the number of vertices) in the largest
clique in G. Draw a graph G, and mark in it the critical coloring
and the largest clique, for each of the following values of
(chi(G),cl(G)): (3,2), (4,2)*, (3,3), (4,3), (5,3)*.
The cases marked with a "*" are not that easy.

Compare briefly two coloring bound heuristics to prune the search
space for maximum cliques: the sampling bound and the greedy bound.
Explain why it is not obvious which one leads to a faster
algorithm.
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May 5, 2004