A version of Szemerédi's regularity lemma for multicolored graphs and directed graphs that is suitable for induced graphs

Details A version of Szemerédi's regularity lemma for multicolored graphs and directed graphs that is suitable for induced graphs A version of Szemerédi's regularity lemma for multicolored graphs and directed graphs that is suitable for induced graphs

2011-06-15

arxiv.org/abs/1106.2871v1

Mathematics

Combinatorics

11 pages

Scientific paper

In this manuscript we develop a version of Szemer\'edi's regularity lemma that is suitable for analyzing multicolorings of complete graphs and directed graphs. In this, we follow the proof of Alon, Fischer, Krivelevich and M. Szegedy [\textit{Combinatorica} \textbf{20}(4) (2000) 451--476] who prove a similar result for graphs. The purpose is to extend classical results on dense hereditary properties, such as the speed of the property or edit distance, to the above-mentioned combinatorial objects.

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