English

A recognition algorithm for adjusted interval digraphs

Discrete Mathematics 2018-10-16 v1

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(n4)O(n^4) time, where nn 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(n3)O(n^3). The algorithm produces a min ordering if the given graph is an adjusted interval digraph.

Keywords

Cite

@article{arxiv.1810.06162,
  title  = {A recognition algorithm for adjusted interval digraphs},
  author = {Asahi Takaoka},
  journal= {arXiv preprint arXiv:1810.06162},
  year   = {2018}
}