zbMATH — the first resource for mathematics

Strong independence of graphcopy functions. (English) Zbl 0462.05057
Graph theory and related topics, Proc. Conf. Honour W. T. Tutte, Waterloo/Ont. 1977, 165-172 (1979).
[For the entire collection see Zbl 0453.00012.]
From the introduction: Let \(H\) be a finite graph on \(v\) vertices. We define a function \(c_H\), with domain the set of all finite graphs, by letting \(c_H(G)\) denote the fraction of subgraphs of \(G\) on \(v\) vertices isomorphic to \(H\). Our primary aim is to investigate the behavior of the functions \(c_H\) with respect to each other. We show that \(c_H\) where \(H\) is restricted to be connected, are independent in a strong sense. We also show that, in an asymptotic sense, the \(c_H\) with \(H\) disconnected, may be expressed in terms of the \(c_H\), \(H\) connected.
Reviewer: E.Palmer

05C99 Graph theory