# 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).

Â© BrainMass Inc. brainmass.com March 4, 2021, 7:27 pm ad1c9bdddfhttps://brainmass.com/math/graphs-and-functions/chromatic-numbers-graph-coloring-102261

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

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.