On the Recognition of Fuzzy Circular Interval Graphs
  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. 
Gianpaolo Oriolo, Ugo Pietropaoli, Gautier Stauffer
cs.DM