Characterization and Linear-time Recognition of Paired Threshold Graphs
Data Structures and Algorithms
2019-10-01 v1 Discrete Mathematics
Abstract
In a paired threshold graph, each vertex has a weight, and two vertices are adjacent if their weight sum is large enough and their weight difference is small enough. It generalizes threshold graphs and unit interval graphs, both very well studied. We present a vertex ordering characterization of this graph class, which enables us to prove that it is a subclass of interval graphs. Further study of clique paths of paired threshold graphs leads to a simple linear-time recognition algorithm for the class.
Cite
@article{arxiv.1909.13029,
title = {Characterization and Linear-time Recognition of Paired Threshold Graphs},
author = {Guozhen Rong and Yixin Cao and Jianxin Wang},
journal= {arXiv preprint arXiv:1909.13029},
year = {2019}
}