diff --git a/src/blossomv.jl b/src/blossomv.jl
index da1e2d4..545893e 100644
--- a/src/blossomv.jl
+++ b/src/blossomv.jl
@@ -1,6 +1,6 @@
 """
-    minimum_weight_perfect_matching(g, w::Dict{Edge,Real})
-    minimum_weight_perfect_matching(g, w::Dict{Edge,Real}, cutoff)
+    minimum_weight_perfect_matching(g, w::Dict{Edge,U<:Real})
+    minimum_weight_perfect_matching(g, w::Dict{Edge,U<:Real}, cutoff)
 
 Given a graph `g` and an edgemap `w` containing weights associated to edges,
 returns a matching with the mimimum total weight among the ones containing
@@ -16,7 +16,9 @@ excluding edges with weights higher than the cutoff.
 
 The returned object is of type `MatchingResult`.
 
-In case of error try to change the optional argument `tmaxscale` (default is `tmaxscale=10`).
+If there is no matching, the returned weight will be `typemax(U)` and no vertex will be matched
+
+In case of error try to change the optional argument `tmaxscale` (default is `tmaxscale=2*nv(g)`).
 """
 function minimum_weight_perfect_matching end
 
@@ -30,16 +32,21 @@ function minimum_weight_perfect_matching(g::Graph, w::Dict{E,U}, cutoff, kws...)
     return minimum_weight_perfect_matching(g, wnew; kws...)
 end
 
-function minimum_weight_perfect_matching(g::Graph, w::Dict{E,U}; tmaxscale=10.) where {U<:AbstractFloat, E<:Edge}
+function minimum_weight_perfect_matching(g::Graph, w::Dict{E,U}; tmaxscale=2*nv(g)) where {U<:AbstractFloat, E<:Edge}
     wnew = Dict{E, Int32}()
     cmax = maximum(values(w))
     cmin = minimum(values(w))
-    tmax = typemax(Int32)  / tmaxscale # /10 is kinda arbitrary,
-                                # hopefully high enough to not occur in overflow problems
+    
+    
+    tmax = typemax(Int32)  / ( (cmax-cmin) * tmaxscale) # tmaxscale = 2*nv(g) is made to ensure that the weights are sufficiently small
+                                                    # compared to typemax(Int32)/3, which is used as an infinite value for non edges
     for (e, c) in w
-        wnew[e] = round(Int32, (c-cmin) / (cmax-cmin) * tmax)
+        wnew[e] = round(Int32, (c-cmin) * tmax)
     end
     match = minimum_weight_perfect_matching(g, wnew)
+    if match.mate[1] == -1 # there is no matching
+        return MatchingResult(typemax(U), match.mate)
+    end
     weight = zero(U)
     for i=1:nv(g)
         j = match.mate[i]
@@ -51,18 +58,35 @@ function minimum_weight_perfect_matching(g::Graph, w::Dict{E,U}; tmaxscale=10.)
 end
 
 function minimum_weight_perfect_matching(g::Graph, w::Dict{E,U}) where {U<:Integer, E<:Edge}
+    @assert nv(g) % 2 == 0
     m = BlossomV.Matching(nv(g))
     for (e, c) in w
         BlossomV.add_edge(m, src(e)-1, dst(e)-1, c)
     end
+
+    # Blossom V needs a feasible matching to work, so we add dummy edges
+    tmax = round(Int, typemax(Int32) / 3)
+    for i in 1:round(Int, nv(g)/2)
+        u, v = 2i-1, 2i
+        if Edge(u, v) ∉ keys(w) && Edge(v, u) ∉ keys(w)
+            BlossomV.add_edge(m, u-1, v-1, tmax)
+        end
+    end
+
     BlossomV.solve(m)
 
     mate = fill(-1, nv(g))
     totweight = zero(U)
     for i=1:nv(g)
         j = BlossomV.get_match(m, i-1) + 1
+        if j == -1 # there is no matching, so we return an infinite weight
+            return MatchingResult(typemax(U), fill(-1, nv(g)))
+        end
         mate[i] = j <= 0 ? -1 : j
         if i < j
+            if !haskey(w, Edge(i, j)) # there is no matching, so we return an infinite weight
+                return MatchingResult(typemax(U), fill(-1, nv(g)))
+            end
             totweight += w[Edge(i,j)]
         end
     end
diff --git a/test/runtests.jl b/test/runtests.jl
index 0beb14f..f00da4f 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -254,6 +254,33 @@ end
     @test match.mate[2] == 3
     @test match.mate[3] == 2
     @test match.weight ≈ 11.5
+
+    # no existing matching
+    g = complete_graph(4)
+    w = Dict{Edge,Int}()
+    w[Edge(1,2)] = 10
+    w[Edge(1,3)] = 20
+    w[Edge(1,4)] = 40
+
+    match = minimum_weight_perfect_matching(g, w)
+    @test match.mate[1] == -1
+    @test match.mate[4] == -1
+    @test match.mate[2] == -1
+    @test match.mate[3] == -1
+    @test match.weight == typemax(Int)
+
+    g = complete_graph(4)
+    w = Dict{Edge,Float64}()
+    w[Edge(1,2)] = 0.5
+    w[Edge(1,3)] = 10.2
+    w[Edge(1,4)] = -5.6
+
+    match = minimum_weight_perfect_matching(g, w)
+    @test match.mate[1] == -1
+    @test match.mate[4] == -1
+    @test match.mate[2] == -1
+    @test match.mate[3] == -1
+    @test match.weight == typemax(Float64)
 end