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Minimum H-Decompositions of Graphs and Its Ramsey Version: A Survey

Conference paper
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Part of the CIM Series in Mathematical Sciences book series (CIMSMS, volume 1)

Abstract

The subject of H-decompositions of graphs was first introduced by Erdős, Goodman and Pósa in 1966. 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 ϕ(n, H) be the smallest number ϕ, such that, any graph G with n vertices admits an H-decomposition with at most ϕ parts. The exact computation of ϕ(n, H) for an arbitrary H is still an open problem. In this paper we will survey recent results about H-decompositions of graphs and we will also introduce its Ramsey or coloured version together with recent results on this problem.

Keywords

Ramsey Version Survey Recent Results Pikhurko Ramsey Numbers Clique Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was partially supported by Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matemática e Aplicações).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Departamento de Matemática and Centro de Matemática e Aplicações, Faculdade de Ciências e TecnologiaUniversidade Nova de LisboaCaparicaPortugal

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