On word-representability of polyomino triangulations
Akrobotu, P. and Kitaev, S. and Masarova, Z. (2015) On word-representability of polyomino triangulations. Siberian Advances in Mathematics, 25 (1). pp. 1-10. ISSN 1934-8126
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Abstract
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)$ is an edge in $E$. Some graphs are word-representable, others are not. It is known that a graph is word-representable if and only if it accepts a so-called semi-transitive orientation. The main result of this paper states that a triangulation of any convex polyomino is word-representable if and only if it is 3-colorable. On the other hand, we provide an example showing that this statement is not true for an arbitrary polyomino. We also show that the graph obtained by replacing each $4$-cycle in a polyomino by the complete graph $K_4$ is word-representable. We make use of semi-transitive orientations to obtain our results.
Creators(s): |
Akrobotu, P., Kitaev, S. ![]() | Item type: | Article |
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ID code: | 51736 |
Keywords: | word representability, semi-transitive orientation, triangulation, (convex) polyomino, Mathematics, Mathematics(all) |
Subjects: | Science > Mathematics |
Department: | Faculty of Science > Computer and Information Sciences |
Depositing user: | Pure Administrator |
Date deposited: | 18 Feb 2015 10:14 |
Last modified: | 01 Jan 2021 05:21 |
Related URLs: | |
URI: | https://strathprints.strath.ac.uk/id/eprint/51736 |
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