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arXiv · 1804.11217

Letter graphs and geometric grid classes of permutations: characterization and recognition

Bogdan Alecu·Vadim Lozin·Dominique de Werra·Viktor Zamaraev
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Abstract

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.

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Bogdan Alecu, Vadim Lozin, Dominique de Werra, Viktor Zamaraev. 2018-04-27. Letter graphs and geometric grid classes of permutations: characterization and recognition. https://arxiv.org/abs/1804.11217

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