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1621 results in 05xxx

Page 82 of 82

  • The lengths of limbs of random trees

  • Part of
  • J. W. Moon
  • Journal:
    Mathematika / Volume 18 / Issue 1 / June 1971
    Published online by Cambridge University Press:
    26 February 2010, pp. 78-81
    Print publication:
    June 1971

  • A tree is a connected graph that has no cycles. If x is any endnode of a tree, then the limb determined by x is the unique path that joins x with the nearest node other than x that does not have degree two in the tree; let l(x) denote the length of this path. (For definitions and results not given here see [2] or [3].) Different endnodes determine different limbs with one exception; when the tree is a path then both endnodes determine the same limb, namely, the tree itself. Our object here is to investigate the distribution of the length of limbs of trees Tn chosen at random from the set of nn-2 trees with n labelled nodes; in particular, it will follow from our results that the length of the longest limb in most trees Tn is approximately log n when n is large.

Page 82 of 82