Department of Mathematics Calendar

Back to Listing

The Department of Mathematics Calendar has moved to Webtools. Anyone may submit an event by clicking the "+" button (upper right). Note: the Sponsor field is required. Just type "n/a"

All events will be reviewed before acceptance. Please email Shelby Koehne if you have any questions about submitting an event.

Note: you may search past and future events by clicking on the magnifying glass icon on the main Calendar page.

For an archive of past events: https://math.illinois.edu/research/seminars-department-calendar

Graph Theory and Combinatorics Seminar: Strong complete minors in digraphs

Event Type
Seminar/Symposium
Sponsor
N/A
Virtual
wifi event
Date
Mar 29, 2022   1:00 pm  
Speaker
Maria Aksenovich (KIT)
Contact
Sean English
Views
11

Kostochka and Thomason independently showed that any graph with average degree Omega (r sqrt{log r}) contains a K_r minor. We consider strong minors in digraphs and ways to force them. A strong →K_r minor is a digraph whose vertex set is partitioned into r parts such that each part induces a strongly-connected subdigraph, and there is at least one edge in each direction between any two distinct parts. We show that any tournament with dichromatic number at least 2r contains a strong →K_r minor, and any tournament with minimum out-degree Omega(r sqrt{log r}) also contains a strong →K_r minor. The latter result is tight up to the implied constant, and may be viewed as a strong-minor analogue to the classical result of Kostochka and Thomason. Lastly, we show that there is no function f: N to N such that any digraph with minimum out-degree at least f(r) contains a strong →K_r minor, but such a function exists when considering dichromatic number.

This is a joint work with Antonio Girao, Richard Snyder, and Lea Weber.

For Zoom information, please contact Sean at SEnglish (at) illinois (dot) edu.

link for robots only