## Rutgers Graduate Student Combinatorics Seminar

This seminar gives graduate students the opportunity to hear and present talks on discrete mathematics, either on topics beyond a standard combinatorics class or on original research. GCS is meant to be a friendly, slightly informal speaking environment where questions are encouraged at all points throughout the talk. We only assume a basic general knowledge of combinatorics (at most, basic combinatorics one might learn in a single semester introductory course), so students in any area are welcome to attend. Speakers for the GCS are welcome (from the math department, other departments, and elsewhere). Please email Kayla Gibson at
kayla.gibson@rutgers.edu

if you are interested in giving a talk.
If you are new to seminars or have trouble with listening to math talks, take a look at these tips for how to get the most out of a talk written by Ravi Vakil. For tips on how to give a good math talk, see these Tips by Jordan Ellenberg. For those interested in feedback on their talk, GCS will have feedback forms available to be filled out.
Generously sponsored by DIMACS.
Click here for information about the seminar and the archive. Speakers below are from the Department of Mathematics, unless otherwise noted.
Next Seminar:
 Date: March 1, 2023 Joshua Schroeder, Guest from Georgia Tech 12:15PM Graduate Student Lounge, 7th Floor, Hill Center (and Zoom) Zoom Link   You can e-mail the organizer for the password. On the 3-colorability of fork-free and triangle-free graphs A graph G is said to satisfy the Vizing bound if \chi(G)\leq\omega(G)+1, where \chi(G) and \omega(G) denote the chromatic number and clique number of G, respectively. It was conjectured by Randerath in 1998 that if G is a triangle-free and fork-free graph, where the fork (also known as trident) is obtained from K_{1,4} by subdividing two edges, then G satisfies the Vizing bound. This talk will outline the proof of this conjecture. In the verification of the proof, a code package for automatically updating graphs about which we have partial information such as forbidden subgraphs/colorability was developed and deployedto manage the case analysis. Therefore thetalk will include a high level description of the code and its role in the proof.

Pet of the Week:

Meet our pet of the week: Sophie! She is very energetic and loves running around in a field, but also likes to snuggle. She also likes eating ice cubes and will come running whenever someone is getting ice. In summary, a very good girl.

Meet Ramsey the new GCS mascot! More pictures will be added here throughout the semester.