On the Independence Number of Random Trees via Tricolourations
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).
Independence number
simply generated tree
Galton-Watson tree
tricolouration
Mathematics of computing~Random graphs
2:1-2:14
Regular Paper
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.
Etienne
Bellin
Etienne Bellin
Ecole Polytechnique, Palaiseau, France
https://orcid.org/0000-0002-8638-1929
10.4230/LIPIcs.AofA.2022.2
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Etienne Bellin
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