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Analysis of three graph parameters for random trees. (English) Zbl 1208.05011
Summary: We consider three basic graph parameters, the node-independence number, the path node-covering number, and the size of the kernel, and study their distributional behavior for an important class of random tree models, namely the class of simply generated trees, which contains, e.g., binary trees, rooted labeled trees, and planted plane trees, as special instances. We can show for simply generated tree families that the mean and the variance of each of the three parameters under consideration behave for a randomly chosen tree of size \(n\) asymptotically \(\sim \mu n\) and \(\sim \nu n\), where the constants \(\mu \) and \(\nu \) depend on the tree family and the parameter studied. Furthermore we show for all parameters, suitably normalized, convergence in distribution to a Gaussian distributed random variable.

05C05 Trees
05C80 Random graphs (graph-theoretic aspects)
Full Text: DOI
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