private static int ComputeSpindleCount(List <int> X, int diamondCount, BitGraph_long HU, BitGraph_long HDL, BitGraph_long HDR, List <List <int> > DU, List <List <int> > DDL, List <List <int> > DDR)
{
var lostSpindlesU = ComputeLostSpindles(X, HU, DU);
var lostSpindlesDL = ComputeLostSpindles(X, HDL, DDL);
var lostSpindlesDR = ComputeLostSpindles(X, HDR, DDR);
return(diamondCount - lostSpindlesU - lostSpindlesDL - lostSpindlesDR);
}
public static int ComputeLostSpindles(List <int> independentSet, BitGraph_long H, List <List <int> > directionDiamonds)
{
var all = (1L << H.N) - 1;
var bases = directionDiamonds.IndicesWhere(d => independentSet.Contains(d[0])).ToInt64();
var tops = directionDiamonds.IndicesWhere(d => independentSet.Contains(d[1])).ToInt64();
var red = all ^ tops;
var blueGreen = all ^ bases;
var tuples = H.MaximalIndependentSubsets(red).Select(R =>
{
var leftover = blueGreen & ~R;
return(new Tuple <long, long, int, int>(R, leftover, BitUsage_long.PopulationCount(R), BitUsage_long.PopulationCount(leftover)));
}).OrderByDescending(t => t.Item3 + t.Item4).ToList();
var best = 0;
var loss = 0;
while (true)
{
var done = true;
foreach (var tuple in tuples)
{
if (tuple.Item3 + tuple.Item4 - loss <= best)
{
break;
}
done = false;
var set = tuple.Item2;
var nset = ~set;
var k = tuple.Item4 - loss;
long subset;
if (loss == 0)
{
subset = set;
}
else
{
subset = 0L;
var q = set;
for (int j = 0; j < k; j++)
{
var bit = q & -q;
subset |= bit;
q ^= bit;
}
}
while (true)
{
if (GraphChoosability_long.IsSubsetTwoColorable(H, subset))
{
best = tuple.Item3 + tuple.Item4 - loss;
break;
}
var u = subset & -subset;
var v = ((subset | nset) + u) & set;
if (v == 0)
{
break;
}
var y = v ^ subset;
var t = BitUsage_long.PopulationCount(y) - 2;
subset = 0L;
var q = set;
for (int j = 0; j < t; j++)
{
var bit = q & -q;
subset |= bit;
q ^= bit;
}
subset |= v;
}
}
if (done)
{
break;
}
loss++;
}
return(H.N - best);
}
static string GeneratePrettyConstraint(List <int> X, List <string> w, int diamondCount, BitGraph_long HU, BitGraph_long HDL, BitGraph_long HDR, List <List <int> > DU, List <List <int> > DDL, List <List <int> > DDR)
{
var spindleCount = ComputeSpindleCount(X, diamondCount, HU, HDL, HDR, DU, DDL, DDR);
return(string.Join(" + ", X.GroupBy(v => w[v]).OrderBy(x => x.Key).Select(x => (x.Count() > 1 ? x.Count().ToString() : "") + x.Key)) + " + " + spindleCount + "s <= 1");
}
public static void Go()
{
File.Delete(WinnersFile);
if (Colors == 5)
{
Winners.Add(Diamond);
}
var tokenSource = new CancellationTokenSource();
var token = tokenSource.Token;
for (int N = MinVertices; N <= MaxVertices; N++)
{
System.Console.ForegroundColor = ConsoleColor.DarkCyan;
System.Console.WriteLine("Checking " + N + " vertex graphs...");
System.Console.ForegroundColor = ConsoleColor.White;
for (var R = MinRingSize; R <= MaxRingSize; R++)
{
System.Console.ForegroundColor = ConsoleColor.DarkGray;
System.Console.WriteLine("Checking ring size " + R + "...");
System.Console.ForegroundColor = ConsoleColor.White;
var path = string.Format(@"C:\Users\landon\Google Drive\research\Graph6\triangulation\disk\triangulation{0}_{1}.g6.tri.weighted.txt", N, R);
if (!File.Exists(path))
{
continue;
}
foreach (var h in path.EnumerateWeightedGraphs())
{
foreach (var g in EnumerateWeightings(h))
{
if (AT)
{
var result = g.HasFOrientation(v => g.Degree(v) - g.VertexWeight[v] - (5 - Colors));
if (result != null)
{
result.Graph.VertexWeight = g.VertexWeight;
var hh = result.Graph.EliminateSinks();
if (hh.E > 0)
{
Winners.Add(hh);
hh.AppendWeightStringToFile(WinnersFile);
System.Console.ForegroundColor = ConsoleColor.Green;
System.Console.WriteLine(string.Format("found {0} AT graph{1} so far", Winners.Count, Winners.Count > 1 ? "s" : ""));
System.Console.ForegroundColor = ConsoleColor.White;
}
}
else
{
}
}
else if (Offline)
{
List <List <int> > badAssignment;
var bg = new BitGraph_long(g.GetEdgeWeights());
if (bg.IsFChoosable(v => bg.Degree(v) - g.VertexWeight[v] - (5 - Colors), out badAssignment))
{
Winners.Add(g);
g.AppendWeightStringToFile(WinnersFile);
System.Console.ForegroundColor = ConsoleColor.Green;
System.Console.WriteLine(string.Format("found {0} choosable graph{1} so far", Winners.Count, Winners.Count > 1 ? "s" : ""));
System.Console.ForegroundColor = ConsoleColor.White;
}
}
else
{
if (g.IsOnlineFChoosable(v => g.Degree(v) - g.VertexWeight[v] - (5 - Colors), token))
{
Winners.Add(g);
g.AppendWeightStringToFile(WinnersFile);
System.Console.ForegroundColor = ConsoleColor.Green;
System.Console.WriteLine(string.Format("found {0} paintable graph{1} so far", Winners.Count, Winners.Count > 1 ? "s" : ""));
System.Console.ForegroundColor = ConsoleColor.White;
}
}
}
}
}
}
}
public static void Go()
{
using (var graphIO = new GraphEnumerator(WinnersFile, MinVertices, MaxVertices))
{
graphIO.FileRoot = @"C:\Users\landon\Google Drive\research\Graph6\graph";
foreach (var g in graphIO.EnumerateGraph6File())
{
if (MaxIndependenceNumber < int.MaxValue)
{
if (g.EnumerateMaximalIndependentSets().Any(mis => mis.Count > MaxIndependenceNumber))
{
continue;
}
}
if (MaxDegree < int.MaxValue && g.MaxDegree > MaxDegree)
{
continue;
}
if (AT)
{
System.Console.Write("checking " + g.ToGraph6() + "...");
if (!g.IsOnlineFGChoosable(v => g.Degree(v) - 1, v => 1))
{
System.Console.WriteLine(" not paintable");
}
else
{
var result = HasFOrientation(g, v => g.Degree(v) - 1, true);
if (result != null)
{
graphIO.AddWinner(g, result.Graph);
System.Console.WriteLine(string.Format(" is d_1-AT"));
}
else
{
System.Console.WriteLine(" not AT");
}
}
}
else if (Offline)
{
if (g.EnumerateMaximalIndependentSets().Any(I => I.Count > 2))
{
continue;
}
System.Console.Write("checking " + g.ToGraph6() + "...");
List <List <int> > badAssignment;
var bg = new BitGraph_long(g.GetEdgeWeights());
System.Console.Write("checking " + g.ToGraph6() + "...");
if (bg.IsFChoosable(v => bg.Degree(v) - 1, out badAssignment))
{
graphIO.AddWinner(g);
System.Console.WriteLine(string.Format(" is {0}-fold d_1-choosable", Fold));
}
else
{
System.Console.WriteLine(" not choosable");
}
}
else
{
if (!DiamondFreeOnly || !g.ContainsInduced(Choosability.Graphs.Diamond))
{
System.Console.Write("checking " + g.ToGraph6() + "...");
if (g.IsOnlineFGChoosable(v => Fold * g.Degree(v) - 1, v => Fold))
{
graphIO.AddWinner(g);
System.Console.WriteLine(string.Format(" is {0}-fold d_1-paintable", Fold));
}
else
{
System.Console.WriteLine(" not paintable");
}
}
else
{
System.Console.WriteLine("skipping due to diamond " + g.ToGraph6());
}
}
}
}
}
public static void Go()
{
using (var graphEnumerator = new GraphEnumerator(WinnersFile, MinVertices, MaxVertices, false))
{
graphEnumerator.FileRoot = @"C:\Users\landon\Google Drive\research\Graph6\graph";
graphEnumerator.WeightCondition = WeightCondition;
graphEnumerator.OnlyExcludeBySpanningSubgraphs = false;
foreach (var g in graphEnumerator.EnumerateGraph6File(Filter, EnumerateWeightings, induced: true))
{
if (MaxIndependenceNumber < int.MaxValue)
{
if (g.EnumerateMaximalIndependentSets().Any(mis => mis.Count > MaxIndependenceNumber))
{
continue;
}
}
if (g.MaxDegree > MaxDegree)
{
continue;
}
if (g.MinDegree < MinDegree)
{
continue;
}
if (Mic)
{
System.Console.Write("checking " + g.ToGraph6() + " with weights [" + string.Join(",", g.VertexWeight) + "] ...");
var micScore = g.Vertices.Sum(v => g.VertexWeight[v] + 1);
if (g.Mic() >= micScore)
{
graphEnumerator.AddWinner(g);
System.Console.WriteLine(string.Format(" is f-KP"));
}
else
{
System.Console.WriteLine(" not f-mic'able");
}
}
else if (AT)
{
System.Console.Write("checking " + g.ToGraph6() + " with weights [" + string.Join(",", g.VertexWeight) + "] ...");
if (!Not)
{
if (!g.IsOnlineFGChoosable(v => g.Degree(v) - g.VertexWeight[v], v => 1))
{
System.Console.WriteLine(" not paintable");
}
else
{
var result = HasFOrientation(g, v => g.Degree(v) - g.VertexWeight[v], true);
if (result != null)
{
if (OddAT)
{
if (Math.Abs(result.Even - result.Odd) % 2 == 1)
{
graphEnumerator.AddWinner(g, result.Graph);
System.Console.WriteLine(string.Format(" is odd f-AT"));
}
else
{
System.Console.WriteLine(string.Format(" not odd f-AT"));
}
}
else
{
graphEnumerator.AddWinner(g, result.Graph);
System.Console.WriteLine(string.Format(" is f-AT"));
}
}
else
{
System.Console.WriteLine(" not AT");
}
}
}
else
{
var good = !g.IsOnlineFGChoosable(v => g.Degree(v) - g.VertexWeight[v], v => 1);
var result = HasFOrientation(g, v => g.Degree(v) - g.VertexWeight[v], true);
good |= result == null || OddAT && Math.Abs(result.Even - result.Odd) % 2 == 0;
if (good)
{
graphEnumerator.AddWinner(g);
System.Console.WriteLine(string.Format(" not f-AT"));
}
else
{
System.Console.WriteLine(" is AT");
}
}
}
else if (Offline)
{
List <List <int> > badAssignment;
var bg = new BitGraph_long(g.GetEdgeWeights());
System.Console.Write("checking " + " with weights [" + string.Join(",", g.VertexWeight) + "] ...");
if (bg.IsFChoosable(v => bg.Degree(v) - g.VertexWeight[v], out badAssignment))
{
graphEnumerator.AddWinner(g);
System.Console.WriteLine(string.Format(" is {0}-fold f-choosable", Fold));
}
else
{
System.Console.WriteLine(" not choosable");
}
}
else
{
System.Console.Write("checking " + " with weights [" + string.Join(",", g.VertexWeight) + "] ...");
if (!Not)
{
if (g.IsOnlineFGChoosable(v => Fold * g.Degree(v) - g.VertexWeight[v], v => Fold))
{
graphEnumerator.AddWinner(g);
System.Console.WriteLine(string.Format(" is {0}-fold f-paintable", Fold));
}
else
{
System.Console.WriteLine(" not paintable");
}
}
else
{
if (!g.IsOnlineFGChoosable(v => Fold * g.Degree(v) - g.VertexWeight[v], v => Fold))
{
graphEnumerator.AddWinner(g);
System.Console.WriteLine(string.Format(" is not {0}-fold f-paintable", Fold));
}
else
{
System.Console.WriteLine(" paintable");
}
}
}
}
}
if (Not)
{
EliminateDoubleEdgeNotSubdivisions.Go(WinnersFile, AT);
}
else
{
EliminiteDoubleEdgeSubdivisions.Go(WinnersFile);
}
}
