Color the map so no two neighbors match, using as few colors as possible. A deceptively hard problem behind scheduling, frequencies, and compilers.
Graph ColoringLive
the chromatic number
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Graph coloring assigns colors to nodes so that no edge connects two of the same color, using as few colors as possible. The greedy algorithm colors nodes in order, picking the lowest color not used by a neighbor. It models scheduling exams, assigning radio frequencies, and register allocation in compilers — all cases where conflicting items must be separated.
Reading this result: Two colors suffice here, which means the graph has no odd cycle — it is bipartite, the easiest case to schedule with zero conflicts.
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How it works
Graph coloring assigns colors to nodes so no edge joins two of the same color, minimizing the number of colors — the chromatic number. The greedy algorithm colors nodes in order with the lowest available color. It models exam timetabling, radio-frequency assignment, and register allocation, where conflicting items must be kept apart. Optimal coloring is NP-hard.
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.