Trac #27079: acyclic_edge_coloring(Graph(3), k=None, value_only=True)…

… should not be 2, should it?

I think that the correct value for
{{{
acyclic_edge_coloring(Graph(3), k=None, value_only=True)
}}}
should be 0, since there is nothing to color.

URL: https://trac.sagemath.org/27079
Reported by: mantepse
Ticket author(s): David Coudert
Reviewer(s): Martin Rubey

src/sage/graphs/graph_coloring.py

@@ -1524,11 +1524,39 @@ def acyclic_edge_coloring(g, hex_colors=False, value_only=False, k=0, solver=Non
         sage: d = acyclic_edge_coloring(g, hex_colors=True)
         sage: sorted(d)
         ['#0066ff', '#00ff66', '#cbff00', '#cc00ff', '#ff0000']
+
+    The acyclic chromatic index of a graph without edge is 0 (:trac:`27079`)::
+
+        sage: from sage.graphs.graph_coloring import acyclic_edge_coloring
+        sage: g = Graph(3)
+        sage: acyclic_edge_coloring(g, k=None, value_only=True)
+        0
+        sage: acyclic_edge_coloring(g, k=None, hex_colors=True)
+        {}
+        sage: acyclic_edge_coloring(g, k=None, hex_colors=False)
+        []
+
+    Empty graph  (:trac:`27079`)::
+
+        sage: from sage.graphs.graph_coloring import acyclic_edge_coloring
+        sage: acyclic_edge_coloring(Graph(), k=None, value_only=True)
+        0
     """
     g._scream_if_not_simple(allow_multiple_edges=True)
 
     from sage.rings.integer import Integer
     from sage.combinat.subset import Subsets
+    from sage.plot.colors import rainbow
+
+    if not g.order() or not g.size():
+        if k == 0:
+            k = 2
+        if value_only:
+            return 0 if k is None else k
+        else:
+            if k is None:
+                return {} if hex_colors else []
+            return {c: [] for c in rainbow(k)} if hex_colors else [copy(g) for _ in range(k)]
 
     if k is None:
         k = max(g.degree())
@@ -1549,8 +1577,6 @@ def acyclic_edge_coloring(g, hex_colors=False, value_only=False, k=0, solver=Non
     elif not k:
         k = max(g.degree()) + 2
 
-    from sage.plot.colors import rainbow
-
     p = MixedIntegerLinearProgram(solver=solver)
 
     # c is a binary variable such that c[i,(u,v)] = 1 if and only if (u,v) is
@@ -1594,7 +1620,10 @@ def E(x, y):
 
     except MIPSolverException:
         if k == max(g.degree()) + 2:
-            raise RuntimeError("It looks like you have found a counterexample to a very old conjecture. Please do not loose it ! Please publish it, and send a post to sage-devel to warn us. We implore you!")
+            raise RuntimeError("It looks like you have found a counterexample to "
+                               "a very old conjecture. Please do not loose it ! "
+                               "Please publish it, and send a post to sage-devel "
+                               "to warn us. We implore you!")
         else:
             raise ValueError("this graph can not be colored with the given number of colors")