On word-representability of polyomino triangulations

P. Akrobotu, S. Kitaev, Z. Masarova

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9 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalSiberian Advances in Mathematics
Volume25
Issue number1
DOIs
Publication statusPublished - 27 Feb 2015

Keywords

  • word representability
  • semi-transitive orientation
  • triangulation
  • (convex) polyomino

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