# Chromatic Numbers and Graph Coloring

Let G1 be a graph such that every two odd cycles intersect. Prove that X(G)=<5.

(The minimum integer for which a graph is k-colorable is called the vertex chromatic number, or simply the chromatic number of , and is denote by , this problem is about graph coloring).

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Let be a graph such that every two odd cycles intersect. Prove that .

(The minimum integer for which a graph is -colorable is called the vertex chromatic number, or simply the chromatic number of , and is denote by , this problem is about graph coloring).

Please your proof have to be perfect proof, this means ...

#### Solution Summary

Chromatic Numbers and Graph Coloring are investigated. The vertex chromatic numbers are determined.