On the Recognition of Fuzzy Circular Interval Graphs

TL;DR

This paper introduces a polynomial-time algorithm for recognizing fuzzy circular interval graphs and constructing their representations, expanding the understanding of this subclass of claw-free graphs.

Contribution

It presents the first efficient recognition algorithm for fuzzy circular interval graphs and details how to construct their representations.

Findings

Polynomial-time recognition algorithm developed

Algorithm effectively constructs graph representations

Advances understanding of fuzzy circular interval graphs

Abstract

Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.