Chromatic Number Estimator
Estimate the chromatic number of a graph using Brook's theorem and greedy coloring bounds.
Inputs
Results
Greedy Coloring Estimate
4
Brook's Bound
4
Upper Bound (Δ+1)5
How to Use This Calculator
- Enter the number of Vertices and Edges in your graph.
- Input the Maximum Degree of any vertex.
- Review the Upper Bound (Max Degree + 1) from Vizing's theorem and the Brooks Bound for non-complete, non-odd-cycle graphs.
- Check the Greedy Coloring Estimate — this is a practical upper bound for sparse graphs.
- Use these bounds to determine the minimum colors needed before running an exact coloring algorithm.
What each input means
- Vertices
- Number of vertices in the graph
- Edges
- Number of edges in the graph
- Max Degree (Δ)
- Maximum vertex degree in the graph
How this is calculated
Worked example, using the default values
- Identify Input ParametersVertices = 8, Edges = 12, Max Degree (Δ) = 4 = 3 input(s) provided
- Calculate Greedy Coloring EstimateGreedy Coloring Estimate = min(greedyEstimate4 = 4
- Calculate Brook's BoundBrook's Bound4 = 4
- Calculate Upper BoundUpper Bound5 = 5
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators.
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