Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, June 09, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Jan Foniok

Interlacing adjoints on directed graphs

A theorem attributed to Hasse, Gallai, Roy and/or Vitaver claims that every orientation of every non-k-colourable graph contains a long directed path or a directed cycle (so it contains a homomorphic image of a long directed path), where "long" means "with at least k+1 vertices". We extend this theorem and prove that there is a family P of oriented paths with unbounded algebraic height such that every orientation of every non-4-colourable graph contains a homomorphic image of every path in P. (algebraic height = #forward arcs - #backward arcs) The motivation for this work is Hedetniemi's product- colouring conjecture (but probably I will not have time to discuss it); the method is "adjoint functors" (and I certainly want to discuss that).

Joint work with J. Nešetřil and C. Tardif.

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