added chromatic coloring stuff

src/GraphInvariants.jl

@@ -35,6 +35,9 @@ struct IndependenceNumber <: AbstractOptimalCardinality end
 struct MaximumClique <: AbstractOptimalSet end
 struct CliqueNumber <: AbstractOptimalCardinality end
 
+struct MinimumProperColoring <: AbstractOptimalSet end
+struct ChromaticNumber <: AbstractOptimalCardinality end
+
 struct MinimumDominatingSet <: AbstractOptimalSet end
 struct DominationNumber <: AbstractOptimalCardinality end
 
@@ -87,6 +90,9 @@ include("basics/from_graphs.jl")
 include("cliques/maximimum_clique.jl")
 include("cliques/clique_number.jl")
 
+include("chromatic_colorings/proper_colorings.jl")
+include("chromatic_colorings/chromatic_number.jl")
+
 include("degree_sequence_invariants/havel_hakimi_residue.jl")
 
 include("domination/minimum_dominating_sets.jl")
@@ -123,6 +129,9 @@ export IndependenceNumber
 export MaximumClique
 export CliqueNumber
 
+export MinimumProperColoring
+export ChromaticNumber
+
 export MinimumDominatingSet
 export DominationNumber
 export DominationRule

src/chromatic_colorings/chromatic_number.jl

@@ -0,0 +1,15 @@
+
+"""
+    compute(::Type{ChromaticNumber}, g::AbstractGraph{T}) where T <: Integer
+
+Return the chromatic number of `g`.
+
+"""
+function compute(
+    ::Type{ChromaticNumber},
+    g::AbstractGraph{T};
+    optimizer = HiGHS.Optimizer
+) where T <: Int
+    min_prop_coloring = compute(MinimumProperColoring, g; optimizer=optimizer)
+    return length(unique(values(min_prop_coloring)))
+end

src/chromatic_colorings/proper_colorings.jl

@@ -0,0 +1,52 @@
+function compute(
+    ::Type{MinimumProperColoring},
+    g::AbstractGraph{T};
+    optimizer = HiGHS.Optimizer
+) where T <: Integer
+
+    # Instantiate the optimization model.
+    model = Model(optimizer)
+    JuMP.set_silent(model)
+
+    # Get the vertices and edges of `g`.
+    V = vertices(g)
+    E = edges(g)
+
+    # Decision variable for each vertex and color.
+    @variable(model, x[V, V], Bin)
+    @variable(model, y[V], Bin)
+
+    # Constraint: Each vertex gets exactly one color
+    @constraint(model, [v = V], sum(x[v, k] for k in V) == 1)
+
+    # Constraint: Adjacent vertices cannot have the same color
+    for e in E
+        u, v = src(e), dst(e)
+        @constraint(model, [k = V], x[u, k] + x[v, k] <= 1)
+    end
+
+    # Constraint: If a vertex is colored with k, color k is used
+    @constraint(model, [v = V, k = V], x[v, k] <= y[k])
+
+    # Constraint: Use the sequential nature of colors. A color k can be used only if color k-1 is used
+    for k = 2:nv(g)
+        @constraint(model, y[k] <= y[k-1])
+    end
+
+    # Objective: Minimize the number of colors used
+    @objective(model, Min, sum(y))
+
+    optimize!(model)
+
+    # Extracting the color for each vertex
+    vertex_colors = Dict{Int, Int}()
+    for v in V
+        for k in V
+            if value(x[v, k]) > 0.5  # using 0.5 as a threshold due to potential numerical issues
+                vertex_colors[v] = k
+                break
+            end
+        end
+    end
+    return vertex_colors
+end