Graph Theory: Lecture No. 14
(Brooks 1941) Let Gbe a connected graph. If
Gis neither complete nor and odd cycle, then
χ(G)≤∆(G).
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Odd Cycle - Graph Theory - Lecture Slides, Slides of Design Patterns
The key points discuss in the Graph theory, which I found very informative are: Odd Cycle, Connected Graph, Neither Complete, Every Integer, Graph, Chromatic Number, Girth, Constructible, Non-Adjacent, K-Constructible Subgraph
Typology: Slides
2012/2013
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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.