coloring document (#95)

docs/make.jl

@@ -28,6 +28,7 @@ makedocs(;
         "Interfaces" => ["models.md", "topology.md", "rules.md"],
         "Models" => [
             "models/CircuitSAT.md",
+            "models/Coloring.md",
             "models/Factoring.md",
             "models/SpinGlass.md"          
         ],

docs/src/models/Coloring.md

@@ -0,0 +1,26 @@
+# Vertex Coloring
+
+## Problem Definition
+The Vertex Coloring (Coloring) problem is defined on a simple graph. Given k kinds of colors, we need to determine whether we can color all vertices on the graph such that no two adjacent vertices share the same color.
+## Interfaces
+
+To initialize a [`Coloring`](@ref) problem, we need to first define a simple graph and decide the number of colors.
+
+```@repl Coloring
+using ProblemReductions, Graphs
+g = smallgraph(:petersen) # define a simple graph, petersen as example
+
+coloring = Coloring{3}(g)
+```
+We create a petersen graph and take 3 colors here to initialize a Coloring Problem. 
+
+Functions [`variables`](@ref), [`flavors`](@ref), [`num_flavors`](@ref), [`parameters`](@ref) and [`set_parameters`](@ref) are implemented for `Coloring` model. 
+```@repl Coloring
+variables(coloring)
+flavors(coloring)
+```
+
+Also, [`evaluate`](@ref) and [`is_vertex_coloring`](@ref) is also implemented.
+```@repl Coloring
+is_vertex_coloring(coloring.graph,[1,2,3,1,3,2,1,2,3,1]) #random assignment
+```