BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Ramsey arrows for graphs Gunderson, David S.


A simple form of Ramsey's theorem says that for any positive integer $m$, there exists an $n=R(m)$ so that no matter how the pairs of an $n$-set are partitioned into two colours, some $m$-subset has all its pairs the same colour. In terms of graphs, this says if the edges of a $K_n$ are 2-coloured, a monochromatic copy of $K_m$ (as a subgraph) can always be found. Such a statement is often expressed in ``Ramsey arrow'' notation. A short survey of Ramsey arrows for graphs is given, culminating in a characterization found with Rodl and Sauer of those triples $G,H,r$ for which there is an $F$ that arrows $G$ when colouring $H$s with $r$ colours.

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