Algebraic Graph Theory International Webinar (28.9.2021)
v utorok 28.9.2021 o 19:00 hod.
The organizers of the Algebraic Graph Theory International Webinar would like to invite you to join us and other colleagues on September 28, 2021, at 7pm Central European Time, for the next presentation delivered by Martin Škoviera.
The title of Martin's talk: Geometric approach to Berge's conjecture
Abstract:
A fascinating conjecture of Berge suggests that every bridgeless cubic graph can be expressed as a union of at most five perfect matchings. Since three perfect matchings suffice only when the graph is 3-edge-colourable, the remaining cubic graphs fall into two classes: those that can be coveredwith four perfect matchings, and those that need at least five. Understanding the cubic graphs that require more than four perfect matchings to cover their edges is therefore fundamental for any potential approach that might lead to proving or disproving Berge's conjecture. A significant obstacle for this has been the fact that examples of cubic graphs that cannotbe covered with four perfect matchings are extremely rare and difficult to find.
In the talk we outline a theory that describes coverings with four perfect matchings as flows whose flow values represent points and outflow patterns represent lines of a configuration six lines spanned by four points of the 3-dimensional projective space over the 2-element field in general position. This theory provides a powerful tool for investigating the graphs that do not admit such a cover and leads to a number of newresults. Among them are, for instance, unification all known examples and constructions into a single family, offering a great variety of new constructions, or disproving conjectures that attribute certain properties to cubic graphs that cannotbe covered with four perfect matchings.
The talk is based on several recently published papers (and some forthcoming ones) co-authored by Edita Macajova.
Join Zoom Meeting at
https://uni-lj-si.zoom.us/j/92545586220?pwd=Vjc4cytxaVBFbFJXY0Q4L2RhOUZHZz09
Meeting ID: 925 4558 6220
Passcode: 117532
Further details may be found at http://euler.doa.fmph.uniba.sk/AGTIW.html
where you can also find the slides and the recordings of our previous presentations. Also, if you wish to advertise an AGT friendly conference on this page, please send us the link.
Hoping to see you at the webinar, and wishing you all the best.
This is the first talk of the webinar after the summer in the Northern Hemisphere, and the plan is to continue on a bi-weekly basis from now on. It is time to be AGTIW again.
Isabel Hubard, Robert Jajcay and Primoz Potocnik