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{\bf Maria Axenovich}
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{\bf On Subgraphs Induced by Transversals in Vertex-Partitions of Graphs}
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For a fixed graph $H$ on $k$ vertices, we investigate the graphs, $G$,
such that for any partition of the vertices of $G$ into $k$ color
classes, there is a transversal of that partition inducing $H$. For
every integer $k\geq 1$, we find a family ${\cal F}$ of at most
six graphs on $k$ vertices such that the following holds. If $H\notin
{\cal F}$, then for any graph $G$ on at least $4k-1$ vertices,
there is a $k$-coloring of vertices of $G$ avoiding totally
multicolored induced subgraphs isomorphic to $H$. Thus, we provide a
vertex-induced anti-Ramsey result, extending the induced-vertex-Ramsey
theorems by Deuber, R\"odl et al.
\bye