Linear Bounds for Cycle-free Saturation Games

@article{English2022LinearBF,
  title={Linear Bounds for Cycle-free Saturation Games},
  author={Sean English and Tom'avs Masavr'ik and Grace McCourt and Erin Meger and Michael S. Ross and Sam Spiro},
  journal={ArXiv},
  year={2022},
  volume={abs/2108.05295}
}
Given a family of graphs $\mathcal{F}$, we define the $\mathcal{F}$-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 $\mathcal{F}$. 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 let $\textrm{sat}_g(n,\mathcal{F… 

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Project Description Sam Spiro

Broadly speaking, questions in extremal combinatorics ask how large or small a combinatorial object can be. For example, a classical theorem of Mantel’s [20] states that every n-vertex triangle-free

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Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully