arXiv:2608. 11211v1 Announce Type: new Abstract: Conway's 99-graph problem asks whether a strongly regular graph with parameters $\mathrm{srg}(99,14,1,2)$ exists.
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arXiv:2608. 08154v1 Announce Type: cross Abstract: The Zarankiewicz number Z(m,n,s,t) is the maximum number of edges in a bipartite graph with parts of orders m and n containing no copy of Ks,t.
arXiv:2606. 24421v1 Announce Type: new Abstract: Spectral filtering recently delivered substantial pruning for \emph{static} subgraph matching: Laplacian interlacing rejects candidates whose neighborhoods cannot host the query.
arXiv:2607. 23500v1 Announce Type: cross Abstract: Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming.
arXiv:2608. 08103v1 Announce Type: new Abstract: Smooth acyclicity constraints answer whether a weighted support is a DAG, whereas structure learning asks which support change should be made.
arXiv:2607. 21517v1 Announce Type: cross Abstract: The Shannon capacity $\Theta(G)$ of a graph $G$ quantifies the maximum rate at which information can be transmitted with zero error over a noisy channel.
arXiv:2607. 10194v1 Announce Type: cross Abstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\Sigma_{\mathrm{HG}}$.