Graph Theory & Combinatorics: Linear Bounds for Cycle-free Saturation Games

Event Type

Seminar/Symposium

Sponsor

n/a

Location

345 AH

Date

Sep 21, 2021   1:00 pm  

Speaker

Grace McCourt (UIUC)

Contact

Sean English

E-Mail

senglish@illinois.edu

Views

13

Abstract: Given a family of graphs F, we define the F-saturation game as follows. Two players alternate adding edges to an initially empty graph on n vertices, with the only constraint being that neither player can add an edge that creates a subgraph in F. The game ends when no more edges can be added to the graph. One of the players wishes to end the game as quickly as possible, while the other wishes to prolong the game. We will consider the number of edges that are in the final graph when both players play optimally.

 

In general there are very few non-trivial bounds on the order of magnitude of the number of edges in the final graph. In this talk, we discuss collections of infinite families of cycles such that the number of edges that are in the final graph has linear growth rate. This is joint work with Sean English, Tomáš Masařik, Erin Meger, Michael Ross, and Sam Spiro.