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Path node-covering constants for certain families of trees

Published online by Cambridge University Press:  24 October 2008

A. Meir  and
J. W. Moon
A. Meir
Affiliation:
University of Alberta, EdmontonUniversity of the WitwatersrandJohannesburg
J. W. Moon
Affiliation:
University of Alberta, EdmontonUniversity of the WitwatersrandJohannesburg
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Extract

1. introduction. A set P of disjoint paths in a graph G is a node-covering of G if every node of G is in a path in P. (For definitions not given here see (5) or (11).) The path (node-covering) number of G is the smallest possible number p(G) of paths in such a node-covering of G. The problem of determining the path number of a graph was considered in (1) and (4) for undirected graphs and in (2) for directed graphs. In particular, an algorithm for determining the path number of a tree was given in (1) and (4). If ℱ denotes some family of trees, let μ(n) = μℱ(n) denote the average value of p(T) over all trees T in ℱ with n nodes. Our object here is to show the existence and to determine the value of the path (node-covering) constant

for certain families ℱ of trees. The arguments are similar to those used in (7), (8), and (9), where some other parameters, associated with families of trees, were investigated.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 3 , November 1978 , pp. 519 - 530
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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