general fixes

Author: pkj-m

src/coloring/greedy_star1_coloring.jl

@@ -5,7 +5,7 @@
     no two vertices connected by an edge have the same
     color using greedy approach. The number of colors
     used may be equal or greater than the chromatic
-    number χ(G) of the graph.
+    number `χ(G)` of the graph.
 
     A star coloring is a special type of distance - 1  coloring,
     For a coloring to be called a star coloring, it must satisfy
@@ -19,27 +19,27 @@
     In other words, every path on four vertices uses at least three
     colors.
 
-    reference: What Color is your Jacobian?, pg 662
+    Reference: Gebremedhin AH, Manne F, Pothen A. **What color is your Jacobian? Graph coloring for computing derivatives.** SIAM review. 2005;47(4):629-705.
 """
-function greedy_star1_coloring(G::VSafeGraph)
-    V = nv(G)
-    color = zeros(Int64, V)
+function greedy_star1_coloring(g::LightGraphs.AbstractGraph)
+    v = nv(g)
+    color = zeros(Int64, v)
 
-    forbiddenColors = zeros(Int64, V+1)
+    forbiddenColors = zeros(Int64, v+1)
 
-    for vertex_i = 1:V
+    for vertex_i = vertices(g)
 
-        for w in inneighbors(G, vertex_i)
+        for w in inneighbors(g, vertex_i)
             if color[w] != 0
                 forbiddenColors[color[w]] = vertex_i
             end
 
-            for x in inneighbors(G, w)
+            for x in inneighbors(g, w)
                 if color[x] != 0
                     if color[w] == 0
                         forbiddenColors[color[x]] = vertex_i
                     else
-                        for y in inneighbors(G, x)
+                        for y in inneighbors(g, x)
                            if color[y] != 0
                                 if y != w && color[y] == color[w]
                                     forbiddenColors[color[x]] = vertex_i

src/coloring/greedy_star2_coloring.jl

@@ -5,7 +5,7 @@
     no two vertices connected by an edge have the same
     color using greedy approach. The number of colors
     used may be equal or greater than the chromatic
-    number χ(G) of the graph.
+    number `χ(G)` of the graph.
 
     A star coloring is a special type of distance - 1  coloring,
     For a coloring to be called a star coloring, it must satisfy
@@ -19,25 +19,25 @@
     In other words, every path on four vertices uses at least three
     colors.
 
-    reference: What Color is your Jacobian?, pg 663
+    Reference: Gebremedhin AH, Manne F, Pothen A. **What color is your Jacobian? Graph coloring for computing derivatives.** SIAM review. 2005;47(4):629-705.
 
     TODO: add text explaining the difference between star1 and
     star2
 """
-function greedy_star2_coloring(G::VSafeGraph)
-    V = nv(G)
-    color = zeros(Int64, V)
+function greedy_star2_coloring(G::LightGraphs.AbstractGraph)
+    v = nv(g)
+    color = zeros(Int64, v)
 
-    forbiddenColors = zeros(Int64, V+1)
+    forbiddenColors = zeros(Int64, v+1)
 
-    for vertex_i = 1:V
+    for vertex_i = vertices(g)
 
-        for w in inneighbors(G, vertex_i)
+        for w in inneighbors(g, vertex_i)
             if color[w] != 0
                 forbiddenColors[color[w]] = vertex_i
             end
 
-            for x in inneighbors(G, w)
+            for x in inneighbors(g, w)
                 if color[x] != 0
                     if color[w] == 0
                         forbiddenColors[color[x]] = vertex_i