An overview of \((\kappa, \tau)\)-regular sets and their applications

DOI10.1016/j.dam.2018.12.020zbMath1421.05088arXiv1812.11895OpenAlexW2908745051MaRDI QIDQ2328081

Domingos Moreira Cardoso

Publication date: 9 October 2019

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.11895

zbMATH Keywords

perfect matchingHamilton cycleefficient dominating setgraph spectramaximum \(k\)-regular induced subgraph

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Graph theory (05C99) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Eulerian and Hamiltonian graphs (05C45)

Related Items

Subgroup regular sets in Cayley graphs ⋮ A NOTE ON REGULAR SETS IN CAYLEY GRAPHS ⋮ Regular sets in Cayley graphs ⋮ Unnamed Item ⋮ Bounds on signless Laplacian eigenvalues of Hamiltonian graphs

Cites Work

• Efficient domination through eigenvalues
• Spectra of graphs
• Laplacian eigenvectors and eigenvalues and almost equitable partitions
• Spectral results on graphs with regularity constraints
• Main eigenvalues and \((\kappa ,\tau )\)-regular sets
• Unicyclic graphs with exactly two main eigenvalues
• Efficient edge domination problems in graphs
• Problems in algebraic combinatorics
• Equitable bipartitions of graphs and related results
• Independent sets with domination constraints
• Maximum \(k\)-regular induced subgraphs
• Relations between (κ, τ)-regular sets and star complements
• Graphs with least eigenvalue -2 attaining a convex quadratic upper bound for the stability number
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