Akrobotu, P. and Kitaev, S. and Masarova, Z. (2015) On word-representability of polyomino triangulations. Siberian Advances in Mathematics, 25 (1). pp. 1-10.
Akrobotu_etal_SAM_2015_On_word_representability_of_polyomino_triangulations.pdf - Accepted Author Manuscript
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.
|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 Apr 2017 17:09|