DeepAI AI Chat
Log In Sign Up

Characterization and Linear-time Recognition of Paired Threshold Graphs

09/28/2019
by   Guozhen Rong, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

09/20/2019

Linear-Time Recognition of Double-Threshold Graphs

A graph G = (V,E) is a double-threshold graph if there exist a vertex-we...
03/15/2021

Unit Disk Representations of Embedded Trees, Outerplanar and Multi-Legged Graphs

A unit disk intersection representation (UDR) of a graph G represents ea...
10/15/2018

A recognition algorithm for adjusted interval digraphs

Min orderings give a vertex ordering characterization, common to some gr...
07/18/2019

Linear-semiorders and their incomparability graphs

A linear-interval order is the intersection of a linear order and an int...
10/08/2019

Fast Diameter Computation within Split Graphs

When can we compute the diameter of a graph in quasi linear time? We add...
04/14/2018

Interval-Like Graphs and Digraphs

We unify several seemingly different graph and digraph classes under one...
02/27/2018

Constructing graphs with limited resources

We discuss the amount of physical resources required to construct a give...