P. Erd?s, A. W. Goodman and L. Pósa, “The Representation of a Graph by Set Intersections,” Canadian Journal of Mathematics, Vol. 18, 1966, pp. 106-112. doi:10.4153/CJM-1966-014-3

has been cited by the following article:

• TITLE: The H-Decomposition Problem for Graphs

  AUTHORS: Teresa Sousa

  KEYWORDS: Graph Decompositions; Weighted Graph Decompositions; Monochromatic Graph Decompositions; Turán Graph; Ramsey Numbers

  JOURNAL NAME: Applied Mathematics, Vol.3 No.11, November 20, 2012

  ABSTRACT: The concept of H-decompositions of graphs was first introduced by Erd?s, Goodman and Pósa in 1966, who were motivated by the problem of representing graphs by set intersections. Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let Ф(n,H) be the smallest number Ф, such that, any graph of order n admits an H-decomposition with at most Ф parts. The exact computation of Ф(n,H) for an arbitrary H is still an open problem. Recently, a few papers have been published about this problem. In this survey we will bring together all the results about H-decompositions. We will also introduce two new related problems, namely Weighted H-Decompositions of graphs and Monochromatic H-Decom- positions of graphs.