In this paper, we reveal an intriguing relationship between two seemingly
unrelated notions: letter graphs and geometric grid classes of permutations. An
important property common for both of them is well-quasi-orderability,
implying, in a non-constructive way, a polynomial-time recognition of geometric
grid classes of permutations and k-letter graphs for a fixed k. However,
constructive algorithms are available only for k=2. In this paper, we present
the first constructive polynomial-time algorithm for the recognition of
3-letter graphs. It is based on a structural characterization of graphs in
this class.Comment: arXiv admin note: text overlap with arXiv:1108.6319 by other author