On the Helly Subclasses of Interval Bigraphs and Circular Arc Bigraphs

Groshaus, Marina; Guedes, André Luiz Pires; Kolberg, Fabricio Schiavon

doi:10.1007/978-3-030-61792-9_50

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While their non-bipartite counterpart is a widely studied class of intersection graphs, circular arc bigraphs remain a relatively unexplored subject. Most results on the class and its subclasses are quite recent, and include matrix-based characterizations for the class and its proper and unit subclasses [1], efficient recognition algorithms for the proper [9] and Helly subclasses [3], and forbidden graph characterizations for some subclasses of the Helly subclass [4].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Subclass Hierarchy on Circular Arc Bigraphs

Groshaus¹,

Guedes²,

Kolberg³

2022

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

“…The relationships that remain to be explored are shown in detail in [4], where the following couple of theorems are proven.…”

mentioning

confidence: 99%