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R. E. Greenwood and A. M. Gleason, “Combinatorial Relations and Chromatic Graphs,” Canadian Journal of Mathematics, Vol. 7, 1955, pp. 1-7. doi:10.4153/CJM-1955-001-4

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.