Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, January 10, 2013, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Jan Foniok (Queen's University)

**Theorem (Geller, Stahl):** Let *G* be a graph. Then the lexicographic product *G*[*K*_{2}] is *n*-colourable if and only if *G* admits a homomorphism to the Kneser graph *K*(*n*,2).

**Theorem (El-Zahar, Sauer):** For two graphs *G* and *H*, the categorial product *G* × *H* is *n*-colourable if and only if *G* admits a homomorphism to the exponential graph *K _{n}^{H}*.

What do these two theorems have in common? Each is an example of the same phenomenon, known in category theory as *adjoint functors*. I will explain what they are and show some other applications, such as a circular version of the Gallai–Roy (–Hasse–Vitaver) Theorem.

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