Minimal decompositions of graphs into mutually isomorphic subgraphs

F. R.K. Chung, P. Erdos, R. L. Graham

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Suppose G n={G 1, ..., G k } is a collection of graphs, all having n vertices and e edges. By a U-decomposition of G n we mean a set of partitions of the edge sets E(G t ) of the G i, say E(G t )== {Mathematical expression} E ij, such that for each j, all the E ij, 1≦i≦k, are isomorphic as graphs. Define the function U(G n) to be the least possible value of r a U-decomposition of G n can have. Finally, let U k (n) denote the largest possible value U(G) can assume where G ranges over all sets of k graphs having n vertices and the same (unspecified) number of edges. In an earlier paper, the authors showed that {Mathematical expression} In this paper, the value of U k (n) is investigated for k>2. It turns out rather unexpectedly that the leading term of U k (n) does not depend on k. In particular we show {Mathematical expression}

Original languageEnglish
Pages (from-to)13-24
Number of pages12
JournalCombinatorica
Volume1
Issue number1
DOIs
Publication statusPublished - Mar 1 1981

Keywords

  • AMS subject classification (1980): 05C35

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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