Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, April 11, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Pascal Su

Hajnal-Szemerédi theorem, but without large independent sets

A classical result by Hajnal and Szemeredi states the minimal degree conditions necessary to guarantee for a graph to contain a K_r-factor. Namely any graph on n vertices, minimum degree \delta(G) > (r-1)n/r and r dividing n has a K_r-factor. This result is tight but the extremal examples are unique in that they have large independent sets and very dense bipartite graphs between these sets. We show that as soon as we move away and forbid these extremal examples, the necessary minimum degree changes.

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