Opened 11 years ago

Closed 10 years ago

# is_cartesian_product

Reported by: Owned by: Nathann Cohen tbd major sage-5.2 graph theory David Joyner, Dima Pasechnik, Rob Beezer sage-5.2.beta0 Nathann Cohen David Coudert N/A

### Description

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

### comment:1 Changed 11 years ago by Nathann Cohen

Component: PLEASE CHANGE → graph theory new → needs_review PLEASE CHANGE → enhancement

### comment:2 Changed 10 years ago by David Coudert

Reviewers: → David Coudert needs_review → needs_work

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
"""
```

### comment:3 Changed 10 years ago by Nathann Cohen

Status: needs_work → needs_review

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

Nathann

### comment:4 Changed 10 years ago by David Coudert

Status: needs_review → positive_review

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

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

### comment:5 Changed 10 years ago by Nathann Cohen

Wouhouuuuuuuu !! Thanks !

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

Nathann

### comment:6 Changed 10 years ago by Jeroen Demeyer

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

### comment:7 Changed 10 years ago by David Coudert

Authors: → Nathann Cohen

### comment:8 Changed 10 years ago by Jeroen Demeyer

Milestone: sage-5.1 → sage-5.2