Sparse Graphs Coalition

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===== 2024 Session 1 : Algebraic, extremal, and structural methods and problems in graph colouring =====

Our overall aim is to bring researchers from algebraic combinatorics and extremal and structural
graph theory together to work on open problems in chromatic graph theory. In the past two
years we have organized virtual AMS meeting sessions ([[https://sites.google.com/view/sp22-enum-extremal-graph-th/home|AMS 2022 session]] and
[[https://sites.google.com/iit.edu/spring2023ams-chromatic/home|AMS 2023 session]]) that have brought together researchers from all parts of combinatorics to
present their work on graph coloring problems with their distinct mathematical perspectives.
These sessions have been a success with participants from Asia, Canada, Europe, and USA.
The topics we will focus on include the chromatic polynomial, chromatic symmetric function,
enumerative functions for various colorings of graphs, variations on graph coloring including list
coloring, DP/correspondence coloring, and independent transversals of graph covers,
algorithms for graph colorings, structural, probabilistic, and algebraic methods for coloring.

==== Organisers ====

[[http://www.math.iit.edu/~kaul/|Hemanshu Kaul]] and [[https://sites.google.com/site/sophiespirkl/|Sophie Spirkl]]

==== Workshop dates ====

19-23 February 2024

==== Participants ====

  * Abhiruk Lahiri
  * Amedeo Sgueglia
  * Anton Bernstheyn
  * Aristotelis Chaniotis
  * Arpan Sadhukhan
  * Aseem Dalal
  * Bartosz Walczak
  * Benjamin Moore
  * Chaya Keller
  * David Mikšaník
  * Evelyne Smith-Roberge
  * Farid Aliniaeifard
  * Fengming Dong
  * Gabriëlle Zwaneveld
  * Hemanshu Kaul
  * Hoang La
  * Hojin Chu
  * Jadwiga Czyżewska
  * Jan Bok
  * Jan van den Heuvel
  * Jana Masarikova
  * Jane Tan
  * Jeffrey Mudrock
  * Jessica McDonald
  * Jingwei Xu
  * Jo Ellis-Monaghan
  * Joshua Erde
  * Kacper Kluk
  * Logan Crew
  * Marcin Briański
  * Marcin Pilipczuk
  * Mathieu Rundstrom
  * Matt Beck
  * Natalie Behague
  * Paloma de Lima
  * Paweł Rzążewski
  * Romain Bourneuf
  * Ronen Wdowinski
  * Rosa Orellana
  * Ross Kang
  * Seokbeom Kim
  * Songling Shan
  * Sophie Spirkl
  * Stephen Hartke
  * Stijn Cambie
  * Tara Abrishami
  * Vilhelm Agdur
  * Wojciech Nadara
  * Wouter Cames van Batenburg
  * Yilin Li
  * Zdeněk Dvořák


Deadline (junior researchers): January 15, 2024 (closed)

Deadline (senior researchers): January 26, 2024 (closed)

==== Schedule (all times Eastern Time, which is UTC-5, so 6 hours less than CET) ====

1. //Monday, 19 February//
  * 9:00 welcome and open problem session
  * 10:30 group formation
2. //Tuesday 20 February//
  * 9:00 talk Joanna Ellis-Monaghan (algebraic aspects)
  * 10:00 group updates
3. //Wednesday 21 February//
  * 9:00 talk Zdenek Dvorak (structural aspects)
  * 10:00 group updates
  * 10:30 talk Anton Bernshteyn (extremal aspects)
4. //Thursday 22 February//
  * 10:00 group updates
5. //Friday, 23 February//
  * 10:00 final updates and close of meeting 

==== Results ====

  * Bourneuf, Masaříková, Nadara, Pilipczuk. Graphs with no long claws: An improved bound for the analog of the Gyárfás’ path argument. https://arxiv.org/abs/2501.13907
  * Kaul, Marciaga, Mudrock. List Coloring the Cartesian Product of a Complete Graph and Complete Bipartite Graph, 2025. https://arxiv.org/abs/2509.16733