On the clique behavior of circulants with three small jumps

Larrión, F.; Pizaña, Miguel A.; Villarroel-Flores, R.

doi:10.1016/j.endm.2009.11.056

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2013

2022

Publication Types

Select...

Other1

Article1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, there are several graph classes for which it is has been proven that a graph in such a class is convergent if and only if it is Helly. Such classes include that of cographs ( [9]), complements and powers of cycles ( [15], [10]), chessboard graphs ( [12]) and circulants with three small jumps ( [11]).…”

Section: Introductionmentioning

confidence: 99%

On the clique behavior and Hellyness of the complements of regular graphs

Villarroel-Flores¹

2022

Preprint

View full text Add to dashboard Cite

A collection of sets is intersecting, if any pair of sets in the collection has nonempty intersection. A collection of sets C has the Helly property if any intersecting subcollection has nonempty intersection. A graph is Helly if the collection of maximal complete subgraphs of G has the Helly property. We prove that if G is a k-regular graph with n vertices such that n > 3k + √ 2k 2 − k, then the complement G is not Helly. We also consider the problem of whether the properties of Hellyness and convergence under the clique graph operator are equivalent for the complement of k-regular graphs, for small values of k.

show abstract