Computing shortest 12-representants of labeled graphs

04/15/2023

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by   Asahi Takaoka, et al.

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The notion of 12-representable graphs was introduced as a variant of a well-known class of word-representable graphs. Recently, these graphs were shown to be equivalent to the complements of simple-triangle graphs. This indicates that a 12-representant of a graph (i.e., a word representing the graph) can be obtained in polynomial time if it exists. However, the 12-representant is not necessarily optimal (i.e., shortest possible). This paper proposes an O(n^2)-time algorithm to generate a shortest 12-representant of a labeled graph, where n is the number of vertices of the graph.