Odd Cycle - Graph Theory - Lecture Slides, Slides of Design Patterns

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(Brooks 1941) Let G be a connected graph. If G is neither complete nor and odd cycle, then χ(G ) ≤ ∆(G ).

For every integer k, there exists a graph G with girth g (G ) > k and chromatic number χ(G ) > k.

Let G be a graph and k ∈ N. Then χ(G ) ≥ k if and only if G has a k-constructible subgraph.