@article {IOPORT.06076524, author = {Dellamonica, Domingos and R\"odl, Vojt\v{e}ch}, title = {Distance preserving Ramsey graphs.}, year = {2012}, journal = {Combinatorics, Probability and Computing}, volume = {21}, number = {4}, issn = {0963-5483}, pages = {554-581}, publisher = {Cambridge University Press, Cambridge}, doi = {10.1017/S096354831200003X}, abstract = {Summary: 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: $\text{dist}_{G^*}(x, y) = \text{dist}_{R}(x, y)$ for every $x,y \in V(G^*);$ the colour of each $t$-set in $G^*$ depends only on the graph-distance metric induced in $G$ by the ordered $t$-set.}, identifier = {06076524}, }