Equivalence between Hypergraph Convexities
Joint Authors
Moscarini, Marina
Mezzini, Mauro
Malvestuto, Francesco M.
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-01-15
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
Let G be a connected graph on V.
A subset X of V is all-paths convex (or ap -convex) if X contains each vertex on every path joining two vertices in X and is monophonically convex (or m-convex) if X contains each vertex on every chordless path joining two vertices in X.
First of all, we prove that ap -convexity and m-convexity coincide in G if and only if G is a tree.
Next, in order to generalize this result to a connected hypergraph H, in addition to the hypergraph versions of ap -convexity and m-convexity, we consider canonical convexity (or c-convexity) and simple-path convexity (or sp -convexity) for which it is well known that m-convexity is finer than both c-convexity and sp -convexity and sp -convexity is finer than ap -convexity.
After proving sp -convexity is coarser than c-convexity, we characterize the hypergraphs in which each pair of the four convexities above is equivalent.
As a result, we obtain a convexity-theoretic characterization of Berge-acyclic hypergraphs and of γ-acyclic hypergraphs.
American Psychological Association (APA)
Malvestuto, Francesco M.& Mezzini, Mauro& Moscarini, Marina. 2012. Equivalence between Hypergraph Convexities. ISRN Discrete Mathematics،Vol. 2011, no. 2011, pp.1-22.
https://search.emarefa.net/detail/BIM-499535
Modern Language Association (MLA)
Malvestuto, Francesco M.…[et al.]. Equivalence between Hypergraph Convexities. ISRN Discrete Mathematics No. 2011 (2011), pp.1-22.
https://search.emarefa.net/detail/BIM-499535
American Medical Association (AMA)
Malvestuto, Francesco M.& Mezzini, Mauro& Moscarini, Marina. Equivalence between Hypergraph Convexities. ISRN Discrete Mathematics. 2012. Vol. 2011, no. 2011, pp.1-22.
https://search.emarefa.net/detail/BIM-499535
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-499535