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On the Independence Number of Random Trees via Tricolourations

Author Etienne Bellin

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Etienne Bellin
  • Ecole Polytechnique, Palaiseau, France

Acknowledgements

I am grateful to Igor Kortchemski for his careful reading of the manuscript and for telling me Frederic Chapoton’s suggestion to consider canonical tricolourations of random trees. I am also grateful to the anonymous referees and their useful remarks.

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Etienne Bellin. On the Independence Number of Random Trees via Tricolourations. In 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 225, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.AofA.2022.2

Abstract

We are interested in the independence number of large random simply generated trees and related parameters, such as their matching number or the kernel dimension of their adjacency matrix. We express these quantities using a canonical tricolouration, which is a way to colour the vertices of a tree with three colours. As an application we obtain limit theorems in L^p for the renormalised independence number in large simply generated trees (including large size-conditioned Bienaymé-Galton-Watson trees).

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Random graphs
Keywords
  • Independence number
  • simply generated tree
  • Galton-Watson tree
  • tricolouration

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