Directed Width Parameters and Circumference of Digraphs

This is a short post about the following paper :

  • Shiva Kintali. “Directed Width Parameters and Circumference of Digraphs“. Preprint available on my publications page.

We prove that the directed treewidth, DAG-width and Kelly-width of a digraph are bounded above by its circumference plus one. This generalizes a theorem of Birmele stating that the treewidth of an undirected graph is at most its circumference. 

Theorem : Let G be a digraph of circumference l. Then the directed treewidth, DAG-width and Kelly-width of G are at most l + 1.

The above theorem can be seen as a mini mini mini directed grid minor theorem. I will be using this theorem in future papers to make progress towards a directed grid minor theorem. Stay tuned !!

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s