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Title: An overview of (k,t)-regular sets and their applications
Author: Cardoso, Domingos M.
Keywords: Perfect matching
Hamilton cycle
Efficient dominating set
Maximum k-regular induced subgraph
Graph spectra
Issue Date: 30-Sep-2019
Publisher: Elsevier
Abstract: A (k,t)-regular set is a vertex subset S inducing a k-regular subgraph such that every vertex out of S has t neighbors in S. This article is an expository overview of the main results obtained for graphs with (k,t)-regular sets. The graphs with classical combinatorial structures, like perfect matchings, Hamilton cycles, efficient dominating sets, etc, are characterized by (k,t)-regular sets whose determination is equivalent to the determination of those classical combinatorial structures. The characterization of graphs with these combinatorial structures are presented. The determination of (k,t)-regular sets in a finite number of steps is deduced and the main spectral properties of these sets are described.
Peer review: yes
DOI: 10.1016/j.dam.2018.12.020
ISSN: 0166-218X
Appears in Collections:CIDMA - Artigos
DMat - Artigos
OGTCG - Artigos

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