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We study F-saturation games, first introduced by Furedi, Reimer and Seress in 1991, and named as such by West. The main question is to determine the length of the game whilst avoiding various classes of graph, playing on a large complete graph. We show lower bounds on the length of path-avoiding games, and more precise results for short paths. We show sharp results for the tree avoiding game and the star avoiding game.
We study analogues of $mathcal{F}$-saturation games, first introduced by Furedi, Reimer and Seress in 1991, and named as such by West. We examine analogous games on directed graphs, and show tight results on the walk-avoiding game. We also examine an
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 crea
We look at several saturation problems in complete balanced blow-ups of graphs. We let $H[n]$ denote the blow-up of $H$ onto parts of size $n$ and refer to a copy of $H$ in $H[n]$ as partite if it has one vertex in each part of $H[n]$. We then ask ho
For a graph $H$, a graph $G$ is $H$-induced-saturated if $G$ does not contain an induced copy of $H$, but either removing an edge from $G$ or adding a non-edge to $G$ creates an induced copy of $H$. Depending on the graph $H$, an $H$-induced-saturate
Let $mathcal{C}$ be a family of edge-colored graphs. A $t$-edge colored graph $G$ is $(mathcal{C}, t)$-saturated if $G$ does not contain any graph in $mathcal{C}$ but the addition of any edge in any color in $[t]$ creates a copy of some graph in $mat