{"record":{"id":"8282aa4cb1e10bc5","repo":"TheAlgorithms/C-Sharp","slug":"graph-cannot-be-colored-with-numcolors-color-s-a-larger","errorCode":null,"errorMessage":"Graph cannot be colored with {numColors} color(s). A larger number of colors may be required.","messagePattern":"Graph cannot be colored with (.+?) color\\(s\\)\\. A larger number of colors may be required\\.","errorType":"exception","errorClass":null,"httpStatus":null,"severity":"error","filePath":"Algorithms/Problems/GraphColoring/GraphColoringSolver.cs","lineNumber":99,"sourceCode":"        if (numColors <= 0)\n        {\n            throw new ArgumentException(\"Number of colors must be positive.\", nameof(numColors));\n        }\n\n        // Handle empty graph\n        if (numVertices == 0)\n        {\n            return Array.Empty<int>();\n        }\n\n        var colors = new int[numVertices];\n\n        // Initialize all vertices as uncolored (-1)\n        Array.Fill(colors, -1);\n\n        if (!ColorVertex(adjacencyMatrix, colors, 0, numColors))\n        {\n            throw new ArgumentException(\n                $\"Graph cannot be colored with {numColors} color(s). \" +\n                $\"A larger number of colors may be required.\");\n        }\n\n        return colors;\n    }\n\n    /// <summary>\n    /// Recursively attempts to color vertices using backtracking.\n    /// </summary>\n    /// <param name=\"adjacencyMatrix\">The graph adjacency matrix.</param>\n    /// <param name=\"colors\">Current color assignment for each vertex.</param>\n    /// <param name=\"vertex\">The current vertex to color.</param>\n    /// <param name=\"numColors\">The number of available colors.</param>\n    /// <returns><c>true</c> if a valid coloring is found; otherwise, <c>false</c>.</returns>\n    /// <remarks>\n    /// This method tries each available color for the current vertex. If a color is valid\n    /// (doesn't conflict with adjacent vertices), it proceeds to color the next vertex.","sourceCodeStart":81,"sourceCodeEnd":117,"githubUrl":"https://github.com/TheAlgorithms/C-Sharp/blob/96e2905cab7bc6b33ac0a34ee5bb82ddccbcbb6c/Algorithms/Problems/GraphColoring/GraphColoringSolver.cs#L81-L117","documentation":"ColorGraph performs exhaustive backtracking; if no assignment of numColors colors produces a proper coloring (starting from vertex 0), it concludes the graph's chromatic number exceeds numColors and throws ArgumentException advising a larger color count.","triggerScenarios":"Coloring a bipartite graph with 1 color, an odd cycle with 2 colors, or any graph whose chromatic number is greater than the supplied numColors.","commonSituations":"Underestimating required colors for dense graphs (cliques), scheduling conflicts modeled as graphs where k was set from a fixed constant, test scenarios asserting infeasibility.","solutions":["Increase numColors (e.g. start with the graph's max degree + 1 and retry).","Detect the minimum needed colors iteratively: try k = 1, 2, 3, ... catching ArgumentException until success.","Pre-analyze the graph (clique size, bipartiteness) to pick a sufficient k."],"exampleFix":"// before\nvar colors = solver.ColorGraph(matrix, 2); // odd cycle: fails\n// after\nint[] colors = null;\nfor (var k = 1; k <= matrix.GetLength(0); k++)\n{\n    try { colors = solver.ColorGraph(matrix, k); break; }\n    catch (ArgumentException) { }\n}","handlingStrategy":"try-catch","validationCode":"// Heuristic lower bound: max degree + 1 often suffices\nvar k = Enumerable.Range(0, matrix.GetLength(0)).Max(v => CountRow(matrix, v)) + 1;","typeGuard":null,"tryCatchPattern":"try { colors = solver.ColorGraph(matrix, k); }\ncatch (ArgumentException) { colors = solver.ColorGraph(matrix, k + 1); } // or retry loop","preventionTips":["Estimate chromatic number before choosing k","Prefer incremental k with retry over fixed guesses","Remember odd cycles need 3 colors, cliques need their size"],"tags":["infeasible-problem","graph-coloring","backtracking"],"backgroundTag":"invalid-argument-value","analyzedSha":"96e2905cab7bc6b33ac0a34ee5bb82ddccbcbb6c","analyzedAt":"2026-09-13T17:04:01.438Z","contentChangedAt":"2026-09-13T17:04:01.438Z","schemaVersion":2},"datasetVersion":"2026-09-16T04:17:20.429Z"}