Tag: Graph theory
Exact maximum diameter found for 2-dimensional simplicial complexes
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in MathematicsWhat the study found The study determines the exact maximum diameter for 2-dimensional abstract simplicial complexes on n vertices for every n. It also identifies an infinite sequence of explicit constructions that achieve this bound. Why the authors say this matters The authors present their result as an answer to a problem posed by Santos…
Extremal signed complete graphs with K2,2-minor-free negative subgraphs
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in MathematicsWhat the study found The authors characterize the extremal signed complete graphs that achieve the maximum and second maximum index when the negative-edge-induced subgraph is a K2,2-minor-free spanning subgraph of Kn. Why the authors say this matters The abstract says this work addresses an extremum problem for the index of a signed complete graph based…
Edge version of graph inducibility is determined by fractional independence number
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in MathematicsWhat the study found The study shows that the edge version of inducibility for any graph H satisfies ρ(H,m) = Θ(m^α_f(H)), where α_f(H) is the fractional independence number of H. The authors also give additional bounds and conjectures for paths and cycles. Why the authors say this matters The authors indicate that this result shifts…
Algorithm enumerates maximal balanced quasi-cliques in signed graphs
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in AlgorithmDiscover maximal balanced quasi-clique enumeration for signed graphs. A novel NP-hard algorithm identifies cohesive subgraphs with positive and negative edges using branch-and-bound optimization.
Survey maps graph roles in retrieval-augmented generation
Survey of graph-based techniques in retrieval-augmented generation systems, examining their roles in database construction, algorithms, and reasoning with structured knowledge.
