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The Existence of Exactlym-Coloured Complete Subgraphs

Alan Stacey, Peter Weidl
1999 Journal of combinatorial theory. Series B (Print)  
Acknowledgement The authors would like to thank \Sonderforschungsbereich 343", University of Bielefeld, for its support.  ...  are exactly c-coloured, then there exists a countable in nite complete subgraph H of K !  ...  I(m): For every colouring of the edges of K ! with in nitely many colours there exists a nite complete subgraph of K ! whose edges are exactly mcoloured. Since we can colour all edges of K !  ... 
doi:10.1006/jctb.1998.1855 fatcat:kvmapayzzzfopdxtigss4tr4je

Approximations to m-coloured complete infinite hypergraphs [article]

Teeradej Kittipassorn, Bhargav Narayanan
2016 arXiv   pre-print
We show that for a natural number m and any finite colouring of the edges of the complete graph on N with m or more colours, there is an exactly m̂-coloured complete infinite subgraph for some m̂ satisfying  ...  In the light of this result, we consider the question of how close we can come to finding an exactly m-coloured complete infinite subgraph.  ...  Acknowledgements Some of the research in this paper was carried out while the authors were visitors at Microsoft Research, Redmond.  ... 
arXiv:1310.1386v2 fatcat:qqms2yhs6ne2hg5wszw6whts2u