is_cartesian_product

[nathanncohen]

This patch implements a new method that lets one recognize whether a graph can be written as the cartesian products of some others. A new module is created because the documentation is rather long, and because the first aim was to write the method much more efficiently, at a much lower level.

As usual, the patch would be much harder to review if it were done all at once, and we would need two versions anyway to check the correction of the trickier algorithm.

The aim of this patch is also to obtain better plots of very symmetrical graphs.

Nathann

CC: @wdjoyner @dimpase @rbeezer

Component: graph theory

Author: Nathann Cohen

Reviewer: David Coudert

Merged: sage-5.2.beta0

Issue created by migration from https://trac.sagemath.org/ticket/12917

[dcoudert]

Reviewer: David Coudert

[dcoudert]

comment:2

Hello,

I'm unable to install the patch with sage.5.1.beta1.

--- generic_graph.py
+++ generic_graph.py
@@ -13093,25 +13093,33 @@
     def cartesian_product(self, other):
         """
         Returns the Cartesian product of self and other.
-        
+
         The Cartesian product of `G` and `H` is the graph `L` with vertex set
         `V(L)` equal to the Cartesian product of the vertices `V(G)` and `V(H)`,
         and `((u,v), (w,x))` is an edge iff either - `(u, w)` is an edge of
         self and `v = x`, or - `(v, x)` is an edge of other and `u = w`.
-        
-        EXAMPLES::
-        
+
+        .. SEEALSO::
+
+            - :meth:`~sage.graphs.graph_decompositions.graph_products.is_cartesian_product`
+              -- factorization of graphs according to the cartesian product
+
+            - :mod:`~sage.graphs.graph_decompositions.graph_products`
+              -- a module on graph products.
+
+        EXAMPLES::
+
             sage: Z = graphs.CompleteGraph(2)
             sage: C = graphs.CycleGraph(5)
             sage: P = C.cartesian_product(Z); P
             Graph on 10 vertices
             sage: P.plot() # long time
-        
-        ::
-        
+
+        ::
+
             sage: D = graphs.DodecahedralGraph()
             sage: P = graphs.PetersenGraph()
-            sage: C = D.cartesian_product(P); C    
+            sage: C = D.cartesian_product(P); C
             Graph on 200 vertices
             sage: C.plot() # long time
         """

[nathanncohen]

comment:3

Updated ! It probably needed a rebase after your patch on graph products got merged ! ;-)

Nathann

[dcoudert]

comment:4

The patch is working perfectly (install, tests, functionality, docbuild and display). Nice work!

In another patch, one should do the same for digraphs.

[nathanncohen]

comment:5

Wouhouuuuuuuu !! Thanks !

I am not sure the algorith would work for digraphs though.. Or it is probably easier, I do not know :-)

Nathann

[jdemeyer]

comment:6

Please fill in your real name in the Author / Reviewer fields.

[dcoudert]

Author: Nathann Cohen

[jdemeyer]

Attachment: trac_12917.patch.gz

Rebased to sage-5.1.rc0

[jdemeyer]

Merged: sage-5.2.beta0