Eigenvalues of K1,k-Free Graphs and the Connectivity of Their Independence Complexes

DOI10.1002/jgt.22004zbMath1350.05089OpenAlexW2257025145MaRDI QIDQ2833255

Eli Berger, Noga Alon, Ron Aharoni

Publication date: 17 November 2016

Published in: Journal of Graph Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/jgt.22004

zbMATH Keywords

eigenvaluesindependent transversalshomological connectivity

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Paths and cycles (05C38) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Vertex degrees (05C07)

Related Items (9)

A strengthening of the spectral chromatic critical edge theorem: Books and theta graphs ⋮ On a conjecture of Stein ⋮ On an \(f\)-coloring generalization of linear arboricity of multigraphs ⋮ Fair Representation by Independent Sets ⋮ Unnamed Item ⋮ Two disjoint independent bases in matroid-graph pairs ⋮ Recent progress on graphs with fixed smallest adjacency eigenvalue: a survey ⋮ Some observations on the smallest adjacency eigenvalue of a graph ⋮ Cooperative colorings and independent systems of representatives

Cites Work

• The clique complex and hypergraph matching
• The linear arboricity of graphs
• Domination numbers and homology
• Triangulated spheres and colored cliques
• A condition for matchability in hypergraphs
• Independence complexes of claw-free graphs
• Eigenvalues and homology of flag complexes and vector representations of graphs
• Odd Independent Transversals are Odd
• The intersection of a matroid and a simplicial complex
• Hall's theorem for hypergraphs

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