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On conditions for emergence of a giant tree in a random unlabelled forest
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E. V. Khvorostyanskaya
Published/Copyright:
December 10, 2007
We consider the set of random forests consisting of N rooted trees ordered in one of N! possible ways and of n nonroot unlabelled vertices. As N, n → ∞, we find the limit distributions of the (N – p)/th term of the set of order statistics obtained by arranging the sizes of the trees of a random unlabelled forest in nondescending order for fixed p = 1, 2, … We find that a giant tree (that is, a tree of size n + o(n)) emerges in the only case where N, n → ∞ so that 
Received: 2006-May-25
Published Online: 2007-12-10
Published in Print: 2007-12-11
© de Gruyter
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Articles in the same Issue
- The limit distribution of the size of a giant component in an Internet-type random graph
- On conditions for emergence of a giant tree in a random unlabelled forest
- On the transition of distributions of sums of random variables related to the generalised allocation scheme from one lattice to another
- A multiple optimal stopping rule for sums of independent random variables
- The cycle structure of a random nonhomogeneous hypergraph on the subcritical stage of evolution
- On the structure of the set of reversible cellular automata
- On-line algorithms for packing rectangles into several strips
- An enhanced algorithm to search for low-degree annihilators for a Zhegalkin polynomial
