Brooks' theorem | graph theory | intermediate level

Episode 87.

Brooks' theorem | graph theory | intermediate level.

Branch of mathematics: graph theory.
Difficulty level: intermediate.

Brooks' theorem. For any connected graph $G$ that is not a complete graph ($K_n$ for some $n$) and is not an odd cycle ($C_{2n+1}$ for some $n$), there is an upper bound on the chromatic number of $G$ in terms of its maximum degree: $\Chi(G) \leq \Delta(G)$.

Mathematics. Discrete Mathematics. Combinatorics. Graph theory.
#Mathematics #DiscreteMathematics #Combinatorics #GraphTheory

tags:
mathematics,graph,graph theory,combinatorics,discrete mathematics,coloring,proper coloring,chromatic number,upper bound,bound,degree,maximum degree,subgraph, Brooks,Brooks' theorem,theorem,connected graph,complete graph,odd cycle,cycle

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