Subclass Hierarchy on Circular Arc Bigraphs

Abstract

Circular arc (CA) bigraphs, a bipartite variation of circular arc graphs, are bipartite graphs such that there exists a one-to-one correspondence between their vertices and a family of arcs on a circle such that vertices of opposite partite sets are neighbors precisely if their corresponding arcs intersect. In this paper, we explore the containment relationships between several subclasses of CA bigraphs, including circular convex bipartite (CCB) graphs, as well as the proper and Helly subclasses of CA bigraphs and interval bigraphs.