Color graphs with minimum colors (chromatic number). Build graphs and try to color them or let the algorithm find optimal coloring.
This tool turns graph coloring into something you can see and verify. Build a graph by adding vertices and connecting them with edges, then either color it yourself by clicking or let the tool search for an optimal coloring and report the chromatic number, the fewest colors that keep adjacent vertices different. Because the search tries every assignment, the reported number is the proven minimum, not a heuristic estimate. The surprise most users hit: a valid k-coloring you produce only proves k colors are enough. Whether fewer would work is a separate question, and on graphs like odd cycles the true minimum is usually smaller than a casual attempt suggests.
A concrete input and expected output from the current implementation.
Input
5-cycle: vertices 1-5, edges 12, 23, 34, 45, 51
Expected output
Chromatic number 3. Sample coloring: color A = {1, 3}, color B = {2, 4}, color C = {5}. The 5-cycle is an odd cycle, and odd cycles are exactly the graphs that cannot be split into two color classes, so 2 colors never work. The search finds a valid 3-coloring instead, and since no 2-coloring exists, 3 is the chromatic number.
Click or tap vertices to assign colors from the palette. The tool marks every edge whose two endpoints share a color, so you can iterate until the whole graph is clean. This mode is a puzzle: completing it proves the graph can be colored with the palette size you used, but nothing more. A successful attempt with k colors establishes only that k colors suffice.
The tool's algorithm mode tests colorings with one color, then two, then three, and so on, checking every assignment at each step until a valid coloring appears. The first number that succeeds is the chromatic number, and the tool displays a witness coloring. Because the check is exhaustive, the result is exact; the cost is that search time grows explosively with vertex count.
The four color theorem guarantees 4 colors only for planar graphs, the ones that can be drawn with no crossing edges. A graph containing the complete graph K5 or the utility graph K3,3 is non-planar and can genuinely need more than 4. Your coloring is probably correct; the 4-color promise simply does not apply.
No. Coloring, conflict checking, and the search all run inside the browser page, and no data is sent anywhere. The practical consequence: your graph exists only while the page is open, so closing the tab discards it and you rebuild it next time.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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