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arXiv · 1810.06162

A recognition algorithm for adjusted interval digraphs

Asahi Takaoka
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Abstract

Min orderings give a vertex ordering characterization, common to some graphs and digraphs such as interval graphs, complements of threshold tolerance graphs (known as co-TT graphs), and two-directional orthogonal ray graphs. An adjusted interval digraph is a reflexive digraph that has a min ordering. Adjusted interval digraph can be recognized in $O(n^4)$ time, where $n$ is the number of vertices of the given graph. Finding a more efficient algorithm is posed as an open question. This note provides a new recognition algorithm with running time $O(n^3)$. The algorithm produces a min ordering if the given graph is an adjusted interval digraph.

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Asahi Takaoka. 2018-10-15. A recognition algorithm for adjusted interval digraphs. https://arxiv.org/abs/1810.06162

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