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Distance Preserving Ramsey Graphs


We prove the following metric Ramsey theorem. For any connected graph G endowed with a linear order on its vertex set, there exists a graph R such that in every colouring of the t-sets of vertices of R it is possible to find a copy G* of G inside R satisfying:

distG*(x, y) = distR(x, y) for every x, yV(G*);

the colour of each t-set in G* depends only on the graph-distance metric induced in G by the ordered t-set.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
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