This lecture covers graph theory fundamentals, including terminologies like clique, independent set, and chromatic number. It also discusses Ramsey theory, coloring of complete graphs, and the concept of monochromatic sets in graph coloring.
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The 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that
