Interval-Permutation Segment Graphs

TL;DR

This paper introduces the interval permutation segment (IP-SEG) model, a new graph class generalizing interval and permutation graphs, and provides algorithms for key problems within this framework.

Contribution

The paper defines the IP-SEG model, characterizes related graph classes with forbidden subgraphs, and offers polynomial algorithms for clique and independent set problems.

Findings

Characterization of graph classes via forbidden subgraphs

Polynomial algorithms for clique and independent set problems

Generalization of interval and permutation graph models

Abstract

In this work, we introduce the \emph{interval permutation segment (IP-SEG)} model that naturally generalizes the geometric intersection models of interval and permutation graphs. We study properties of two graph classes that arise from the IP-SEG model and present a family of forbidden subgraphs for these classes. In addition, we present polynomial algorithms for the clique and independent set problems on these classes, when the model is given as part of the input.