Douglas B. West (Illinois Math and Zhejiang Normal University) Reconstruction from the deck of $k$vertex induced subgraphs Abstract: The $k$deck of a graph is its multiset of subgraphs induced by $k$ vertices; we ask whether the $k$deck determines the graph. We show that a complete $r$partite graph is determined by its $(r+1)$deck. Letting $n=V(G)$, we generalize a result of Bollobás by showing that for $l=(1o(1))n/2$, almost every graph $G$ is determined by various sets of ${l+2\choose 2}$ subgraphs with $nl$ vertices. However, when $l=n/2$, the entire $(nl)$deck does not always determine whether $G$ is connected (it fails for $n$vertex paths). We strengthen a result of Manvel by proving for each $l$ that when $n$ is sufficiently large (at least $l^{l^2}$), the $(nl)$deck determines whether $G$ is connected ($n\ge25$ suffices when $l=3$, and $n\le 2l$ cannot suffice). Finally, for every graph $G$ with maximum degree $2$, we determine the least $k$ such that $G$ is reconstructible from its $k$deck, which involves extending a result of Stanley. This is joint work with Hannah Spinoza. 
