Hello everyone. I wanted to share this interesting link on a recently disproved conjecture relating to tensor products: en.wikipedia.org/wiki/Hedetniemi%27s_conjecture👍
My Guess is that the tensor product of 2 disconnected graphs are disconnected . For 2 bipartite graps each vertice in the product set can only connect if they are adjacent in the factor graphs. So since only sets connect to other sets in the factor graph, they can’t connect to the same set in the product graph so it’s bipartite
You're correct for both! For the first one, if either factor graph is disconnected, then the vertices with left/right entries in one connected component cannot connect to those with left/right entries in the other connected component, so the disconnected structure kind of carries over to the tensor product. And you're exactly right about the reason for why the tensor product of bipartite graphs is bipartite. 👍
![What is the Strong Product Of Graphs? [Discrete Mathematics] +3 examples!](http://i.ytimg.com/vi/LO5ynFEd64k/mqdefault.jpg)
![What is the Strong Product Of Graphs? [Discrete Mathematics] +3 examples!](/img/tr.png)
0:00 Definition
1:15 Tensor vs Cartesian product
1:27 Example 1
3:18 Example 2
5:55 Example 3
6:54 Intuition
very interesting topic and great explanation!
Lovely explained!
Thank you for your video! Nice explanation.
You're very welcome 👍
Is tensor product direct product?
Yes. Tensor product is another name for Direct product.
Hello everyone. I wanted to share this interesting link on a recently disproved conjecture relating to tensor products: en.wikipedia.org/wiki/Hedetniemi%27s_conjecture👍
My Guess is that the tensor product of 2 disconnected graphs are disconnected . For 2 bipartite graps each vertice in the product set can only connect if they are adjacent in the factor graphs. So since only sets connect to other sets in the factor graph, they can’t connect to the same set in the product graph so it’s bipartite
You're correct for both! For the first one, if either factor graph is disconnected, then the vertices with left/right entries in one connected component cannot connect to those with left/right entries in the other connected component, so the disconnected structure kind of carries over to the tensor product. And you're exactly right about the reason for why the tensor product of bipartite graphs is bipartite. 👍