diff --git a/Project.toml b/Project.toml
index 6c3eb1cb..2e71e968 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "SparseMatrixColorings"
 uuid = "0a514795-09f3-496d-8182-132a7b665d35"
 authors = ["Guillaume Dalle", "Alexis Montoison"]
-version = "0.4.18"
+version = "0.4.19"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/coloring.jl b/src/coloring.jl
index d5214610..c38ebd26 100644
--- a/src/coloring.jl
+++ b/src/coloring.jl
@@ -1,11 +1,11 @@
 """
-    partial_distance2_coloring(bg::BipartiteGraph, ::Val{side}, order::AbstractOrder)
+    partial_distance2_coloring(bg::BipartiteGraph, ::Val{side}, vertices_in_order::AbstractVector)
 
 Compute a distance-2 coloring of the given `side` (`1` or `2`) in the bipartite graph `bg` and return a vector of integer colors.
 
 A _distance-2 coloring_ is such that two vertices have different colors if they are at distance at most 2.
 
-The vertices are colored in a greedy fashion, following the `order` supplied.
+The vertices are colored in a greedy fashion, following the order supplied.
 
 # See also
 
@@ -17,11 +17,10 @@ The vertices are colored in a greedy fashion, following the `order` supplied.
 > [_What Color Is Your Jacobian? Graph Coloring for Computing Derivatives_](https://epubs.siam.org/doi/10.1137/S0036144504444711), Gebremedhin et al. (2005), Algorithm 3.2
 """
 function partial_distance2_coloring(
-    bg::BipartiteGraph{T}, ::Val{side}, order::AbstractOrder
+    bg::BipartiteGraph{T}, ::Val{side}, vertices_in_order::AbstractVector{<:Integer}
 ) where {T,side}
     color = Vector{T}(undef, nb_vertices(bg, Val(side)))
     forbidden_colors = Vector{T}(undef, nb_vertices(bg, Val(side)))
-    vertices_in_order = vertices(bg, Val(side), order)
     partial_distance2_coloring!(color, forbidden_colors, bg, Val(side), vertices_in_order)
     return color
 end
@@ -54,7 +53,7 @@ function partial_distance2_coloring!(
 end
 
 """
-    star_coloring(g::AdjacencyGraph, order::AbstractOrder, postprocessing::Bool)
+    star_coloring(g::AdjacencyGraph, vertices_in_order::AbstractVector, postprocessing::Bool)
 
 Compute a star coloring of all vertices in the adjacency graph `g` and return a tuple `(color, star_set)`, where
 
@@ -63,7 +62,7 @@ Compute a star coloring of all vertices in the adjacency graph `g` and return a
 
 A _star coloring_ is a distance-1 coloring such that every path on 4 vertices uses at least 3 colors.
 
-The vertices are colored in a greedy fashion, following the `order` supplied.
+The vertices are colored in a greedy fashion, following the order supplied.
 
 If `postprocessing=true`, some colors might be replaced with `0` (the "neutral" color) as long as they are not needed during decompression.
 
@@ -77,7 +76,7 @@ If `postprocessing=true`, some colors might be replaced with `0` (the "neutral"
 > [_New Acyclic and Star Coloring Algorithms with Application to Computing Hessians_](https://epubs.siam.org/doi/abs/10.1137/050639879), Gebremedhin et al. (2007), Algorithm 4.1
 """
 function star_coloring(
-    g::AdjacencyGraph{T}, order::AbstractOrder, postprocessing::Bool
+    g::AdjacencyGraph{T}, vertices_in_order::AbstractVector{<:Integer}, postprocessing::Bool
 ) where {T<:Integer}
     # Initialize data structures
     nv = nb_vertices(g)
@@ -88,7 +87,6 @@ function star_coloring(
     treated = zeros(T, nv)
     star = Vector{T}(undef, ne)
     hub = T[]  # one hub for each star, including the trivial ones
-    vertices_in_order = vertices(g, order)
 
     for v in vertices_in_order
         for (w, index_vw) in neighbors_with_edge_indices(g, v)
@@ -206,7 +204,7 @@ struct StarSet{T}
 end
 
 """
-    acyclic_coloring(g::AdjacencyGraph, order::AbstractOrder, postprocessing::Bool)
+    acyclic_coloring(g::AdjacencyGraph, vertices_in_order::AbstractVector, postprocessing::Bool)
 
 Compute an acyclic coloring of all vertices in the adjacency graph `g` and return a tuple `(color, tree_set)`, where
 
@@ -215,7 +213,7 @@ Compute an acyclic coloring of all vertices in the adjacency graph `g` and retur
 
 An _acyclic coloring_ is a distance-1 coloring with the further restriction that every cycle uses at least 3 colors.
 
-The vertices are colored in a greedy fashion, following the `order` supplied.
+The vertices are colored in a greedy fashion, following the order supplied.
 
 If `postprocessing=true`, some colors might be replaced with `0` (the "neutral" color) as long as they are not needed during decompression.
 
@@ -229,7 +227,7 @@ If `postprocessing=true`, some colors might be replaced with `0` (the "neutral"
 > [_New Acyclic and Star Coloring Algorithms with Application to Computing Hessians_](https://epubs.siam.org/doi/abs/10.1137/050639879), Gebremedhin et al. (2007), Algorithm 3.1
 """
 function acyclic_coloring(
-    g::AdjacencyGraph{T}, order::AbstractOrder, postprocessing::Bool
+    g::AdjacencyGraph{T}, vertices_in_order::AbstractVector{<:Integer}, postprocessing::Bool
 ) where {T<:Integer}
     # Initialize data structures
     nv = nb_vertices(g)
@@ -239,7 +237,6 @@ function acyclic_coloring(
     first_neighbor = fill((zero(T), zero(T), zero(T)), nv)  # at first no neighbors have been encountered
     first_visit_to_tree = fill((zero(T), zero(T)), ne)
     forest = Forest{T}(ne)
-    vertices_in_order = vertices(g, order)
 
     for v in vertices_in_order
         for w in neighbors(g, v)
@@ -527,8 +524,8 @@ function TreeSet(
         # Positions of the first and last vertices in the current tree
         # Note: tree_edge_indices contains the positions of the first and last edges,
         # so we add to add an offset k-1 between edge indices and vertex indices
-        first_vertex = tree_edge_indices[k] + (k-1)
-        last_vertex = tree_edge_indices[k + 1] + (k-1)
+        first_vertex = tree_edge_indices[k] + (k - 1)
+        last_vertex = tree_edge_indices[k + 1] + (k - 1)
 
         # compute the degree of each vertex in the tree
         for index_vertex in first_vertex:last_vertex
diff --git a/src/interface.jl b/src/interface.jl
index f54b5f73..79fe71e9 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -227,10 +227,10 @@ function _coloring(
     decompression_eltype::Type,
     symmetric_pattern::Bool,
 )
-    bg = BipartiteGraph(
-        A; symmetric_pattern=symmetric_pattern || A isa Union{Symmetric,Hermitian}
-    )
-    color = partial_distance2_coloring(bg, Val(2), algo.order)
+    symmetric_pattern = symmetric_pattern || A isa Union{Symmetric,Hermitian}
+    bg = BipartiteGraph(A; symmetric_pattern)
+    vertices_in_order = vertices(bg, Val(2), algo.order)
+    color = partial_distance2_coloring(bg, Val(2), vertices_in_order)
     if speed_setting isa WithResult
         return ColumnColoringResult(A, bg, color)
     else
@@ -246,10 +246,10 @@ function _coloring(
     decompression_eltype::Type,
     symmetric_pattern::Bool,
 )
-    bg = BipartiteGraph(
-        A; symmetric_pattern=symmetric_pattern || A isa Union{Symmetric,Hermitian}
-    )
-    color = partial_distance2_coloring(bg, Val(1), algo.order)
+    symmetric_pattern = symmetric_pattern || A isa Union{Symmetric,Hermitian}
+    bg = BipartiteGraph(A; symmetric_pattern)
+    vertices_in_order = vertices(bg, Val(1), algo.order)
+    color = partial_distance2_coloring(bg, Val(1), vertices_in_order)
     if speed_setting isa WithResult
         return RowColoringResult(A, bg, color)
     else
@@ -266,7 +266,8 @@ function _coloring(
     symmetric_pattern::Bool,
 )
     ag = AdjacencyGraph(A; has_diagonal=true)
-    color, star_set = star_coloring(ag, algo.order, algo.postprocessing)
+    vertices_in_order = vertices(ag, algo.order)
+    color, star_set = star_coloring(ag, vertices_in_order, algo.postprocessing)
     if speed_setting isa WithResult
         return StarSetColoringResult(A, ag, color, star_set)
     else
@@ -283,7 +284,8 @@ function _coloring(
     symmetric_pattern::Bool,
 ) where {R}
     ag = AdjacencyGraph(A; has_diagonal=true)
-    color, tree_set = acyclic_coloring(ag, algo.order, algo.postprocessing)
+    vertices_in_order = vertices(ag, algo.order)
+    color, tree_set = acyclic_coloring(ag, vertices_in_order, algo.postprocessing)
     if speed_setting isa WithResult
         return TreeSetColoringResult(A, ag, color, tree_set, R)
     else
@@ -301,7 +303,8 @@ function _coloring(
 ) where {R}
     A_and_Aᵀ, edge_to_index = bidirectional_pattern(A; symmetric_pattern)
     ag = AdjacencyGraph(A_and_Aᵀ, edge_to_index; has_diagonal=false)
-    color, star_set = star_coloring(ag, algo.order, algo.postprocessing)
+    vertices_in_order = vertices(ag, algo.order)
+    color, star_set = star_coloring(ag, vertices_in_order, algo.postprocessing)
     if speed_setting isa WithResult
         symmetric_result = StarSetColoringResult(A_and_Aᵀ, ag, color, star_set)
         return BicoloringResult(A, ag, symmetric_result, R)
@@ -323,7 +326,8 @@ function _coloring(
 ) where {R}
     A_and_Aᵀ, edge_to_index = bidirectional_pattern(A; symmetric_pattern)
     ag = AdjacencyGraph(A_and_Aᵀ, edge_to_index; has_diagonal=false)
-    color, tree_set = acyclic_coloring(ag, algo.order, algo.postprocessing)
+    vertices_in_order = vertices(ag, algo.order)
+    color, tree_set = acyclic_coloring(ag, vertices_in_order, algo.postprocessing)
     if speed_setting isa WithResult
         symmetric_result = TreeSetColoringResult(A_and_Aᵀ, ag, color, tree_set, R)
         return BicoloringResult(A, ag, symmetric_result, R)
diff --git a/test/suitesparse.jl b/test/suitesparse.jl
index bf3bea04..d69d8a9f 100644
--- a/test/suitesparse.jl
+++ b/test/suitesparse.jl
@@ -20,11 +20,11 @@ using Test
 
 nbunique(x) = length(unique(x))
 
-_N() = NaturalOrder()
-_LF() = LargestFirst()
-_SL() = SmallestLast(; reproduce_colpack=true)
-_ID() = IncidenceDegree(; reproduce_colpack=true)
-_DLF() = DynamicLargestFirst(; reproduce_colpack=true)
+_N(args...) = vertices(args..., NaturalOrder())
+_LF(args...) = vertices(args..., LargestFirst())
+_SL(args...) = vertices(args..., SmallestLast(; reproduce_colpack=true))
+_ID(args...) = vertices(args..., IncidenceDegree(; reproduce_colpack=true))
+_DLF(args...) = vertices(args..., DynamicLargestFirst(; reproduce_colpack=true))
 
 ## Distance-2 coloring
 
@@ -49,13 +49,17 @@ colpack_table_6_7 = CSV.read(
             @test maximum_degree(bg, Val(2)) == row[:Δ2]
         end
         @testset "Natural" begin
-            @test nbunique(partial_distance2_coloring(bg, Val(1), _N())) == row[:N1]
-            @test nbunique(partial_distance2_coloring(bg, Val(2), _N())) == row[:N2]
+            @test nbunique(partial_distance2_coloring(bg, Val(1), _N(bg, Val(1)))) ==
+                row[:N1]
+            @test nbunique(partial_distance2_coloring(bg, Val(2), _N(bg, Val(2)))) ==
+                row[:N2]
         end
         yield()
         @testset "LargestFirst" begin
-            @test nbunique(partial_distance2_coloring(bg, Val(1), _LF())) == row[:LF1]
-            @test nbunique(partial_distance2_coloring(bg, Val(2), _LF())) == row[:LF2]
+            @test nbunique(partial_distance2_coloring(bg, Val(1), _LF(bg, Val(1)))) ==
+                row[:LF1]
+            @test nbunique(partial_distance2_coloring(bg, Val(2), _LF(bg, Val(2)))) ==
+                row[:LF2]
         end
         yield()
         if row[:name] == "af23560"
@@ -67,18 +71,24 @@ colpack_table_6_7 = CSV.read(
             continue
         end
         @testset "SmallestLast" begin
-            @test nbunique(partial_distance2_coloring(bg, Val(1), _SL())) == row[:SL1]
-            @test nbunique(partial_distance2_coloring(bg, Val(2), _SL())) == row[:SL2]
+            @test nbunique(partial_distance2_coloring(bg, Val(1), _SL(bg, Val(1)))) ==
+                row[:SL1]
+            @test nbunique(partial_distance2_coloring(bg, Val(2), _SL(bg, Val(2)))) ==
+                row[:SL2]
         end
         yield()
         @testset "IncidenceDegree" begin
-            @test nbunique(partial_distance2_coloring(bg, Val(1), _ID())) == row[:ID1]
-            @test nbunique(partial_distance2_coloring(bg, Val(2), _ID())) == row[:ID2]
+            @test nbunique(partial_distance2_coloring(bg, Val(1), _ID(bg, Val(1)))) ==
+                row[:ID1]
+            @test nbunique(partial_distance2_coloring(bg, Val(2), _ID(bg, Val(2)))) ==
+                row[:ID2]
         end
         yield()
         @testset "DynamicLargestFirst" begin
-            @test nbunique(partial_distance2_coloring(bg, Val(1), _DLF())) == row[:DLF1]
-            @test nbunique(partial_distance2_coloring(bg, Val(2), _DLF())) == row[:DLF2]
+            @test nbunique(partial_distance2_coloring(bg, Val(1), _DLF(bg, Val(1)))) ==
+                row[:DLF1]
+            @test nbunique(partial_distance2_coloring(bg, Val(2), _DLF(bg, Val(2)))) ==
+                row[:DLF2]
         end
         yield()
     end
@@ -105,7 +115,8 @@ what_table_31_32 = CSV.read(
         @test maximum_degree(bg, Val(1)) == row[:ρmax]
         @test minimum_degree(bg, Val(2)) == row[:κmin]
         @test maximum_degree(bg, Val(2)) == row[:κmax]
-        color_Nb = partial_distance2_coloring(bg, Val(2), NaturalOrder())
+        vertices_in_order = vertices(bg, Val(2), NaturalOrder())
+        color_Nb = partial_distance2_coloring(bg, Val(2), vertices_in_order)
         if length(unique(color_Nb)) == row[:K]
             @test length(unique(color_Nb)) == row[:K]
         else
@@ -133,7 +144,8 @@ what_table_41_42 = CSV.read(
         @test maximum_degree(ag) == row[:Δ]
         @test minimum_degree(ag) == row[:δ]
         postprocessing = false
-        color_N, _ = star_coloring(ag, NaturalOrder(), postprocessing)
+        vertices_in_order = vertices(ag, NaturalOrder())
+        color_N, _ = star_coloring(ag, vertices_in_order, postprocessing)
         @test_skip row[:KS1] <= length(unique(color_N)) <= row[:KS2]  # TODO: find better
         yield()
     end