An overview of (κ,τ)-regular sets and their applications
| Autor: | Domingos M. Cardoso |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Vertex (graph theory)
Applied Mathematics Spectral properties 0211 other engineering and technologies 021107 urban & regional planning 0102 computer and information sciences 02 engineering and technology 01 natural sciences Hamiltonian path Combinatorics symbols.namesake Graph spectra 010201 computation theory & mathematics symbols Discrete Mathematics and Combinatorics Finite set Mathematics Regular sets |
| Zdroj: | Discrete Applied Mathematics. 269:2-10 |
| ISSN: | 0166-218X |
| DOI: | 10.1016/j.dam.2018.12.020 |
| Popis: | A ( κ , τ ) -regular set is a vertex subset S inducing a κ -regular subgraph such that every vertex out of S has τ neighbors in S . This article is an expository overview of the main results obtained for graphs with ( κ , τ ) -regular sets. The graphs with classical combinatorial structures, like perfect matchings, Hamilton cycles, efficient dominating sets, etc., are characterized by ( κ , τ ) -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 ( κ , τ ) -regular sets in a finite number of steps is deduced and the main spectral properties of graphs with these sets are described. |
| Databáze: | OpenAIRE |
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