Applied Mathematics

Volume 3, Issue 11 (November 2012)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.83  Citations  

The H-Decomposition Problem for Graphs

HTML  Download Download as PDF (Size: 145KB)  PP. 1719-1722  
DOI: 10.4236/am.2012.311237    3,611 Downloads   5,389 Views   Citations
Author(s)

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.

Cite this paper

T. Sousa, "The H-Decomposition Problem for Graphs," Applied Mathematics, Vol. 3 No. 11, 2012, pp. 1719-1722. doi: 10.4236/am.2012.311237.

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.