From b221a5d26788e679eb662e28c05fe0a8988cedb8 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <35051714+amontoison@users.noreply.github.com>
Date: Fri, 4 Apr 2025 22:19:23 -0500
Subject: [PATCH 1/2] Update coloring.jl

---
 src/coloring.jl | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/coloring.jl b/src/coloring.jl
index 5f14ece7..0be8879a 100644
--- a/src/coloring.jl
+++ b/src/coloring.jl
@@ -339,9 +339,9 @@ function _grow_star!(
     if p != v  # a neighbor of v with color[w] encountered for the first time
         first_neighbor[color[w]] = (v, w, index_vw)
     else  # merge T_{vw} with a two-colored star being grown around v
-        root1 = find_root!(forest, index_vw)
-        root2 = find_root!(forest, index_pq)
-        root_union!(forest, root1, root2)
+        root_vw = find_root!(forest, index_vw)
+        root_pq = find_root!(forest, index_pq)
+        root_union!(forest, root_vw, root_pq)
     end
     return nothing
 end
@@ -356,10 +356,10 @@ function _merge_trees!(
     # modified
     forest::Forest{<:Integer},
 )
-    root1 = find_root!(forest, index_vw)
-    root2 = find_root!(forest, index_wx)
-    if root1 != root2
-        root_union!(forest, root1, root2)
+    root_vw = find_root!(forest, index_vw)
+    root_wx = find_root!(forest, index_wx)
+    if root_vw != root_wx
+        root_union!(forest, root_vw, root_wx)
     end
     return nothing
 end

From a12c3128c8ce7064931249d67c9bd51af3d0b47b Mon Sep 17 00:00:00 2001
From: Alexis Montoison <35051714+amontoison@users.noreply.github.com>
Date: Fri, 4 Apr 2025 23:31:57 -0500
Subject: [PATCH 2/2] Update coloring.jl

---
 src/coloring.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/coloring.jl b/src/coloring.jl
index 0be8879a..5c4f38a5 100644
--- a/src/coloring.jl
+++ b/src/coloring.jl
@@ -314,10 +314,10 @@ function _prevent_cycle!(
     forbidden_colors::AbstractVector{<:Integer},
     forest::Forest{<:Integer},
 )
-    id = find_root!(forest, index_wx)  # The edge wx belongs to the 2-colored tree T, represented by an edge with an integer ID
-    (p, q) = first_visit_to_tree[id]
+    root_wx = find_root!(forest, index_wx)  # The edge wx belongs to the 2-colored tree T, represented by an edge with an integer ID
+    (p, q) = first_visit_to_tree[root_wx]
     if p != v  # T is being visited from vertex v for the first time
-        first_visit_to_tree[id] = (v, w)
+        first_visit_to_tree[root_wx] = (v, w)
     elseif q != w  # T is connected to vertex v via at least two edges
         forbidden_colors[color[x]] = v
     end