AutoGraphForge is a computational pipeline designed to automate the discovery, refutation, formalization, and proving of graph-theoretic conjectures. It generates conjectures using a Graffiti3 generator, filters out known results with a novelty filter, tests candidates against a large dataset of graphs, and refines surviving conjectures through counterexample search. The pipeline then translates each conjecture into Lean 4, verifies proofs with neural provers, and integrates the results into a formal library.
By J\'an Pastorek
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.
By Koyar Afrasyab
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.
By Minghao Chen, Jiale Zheng
arXiv:2609.16412v1 Announce Type: cross
Abstract: Whitney's theorem allows isomorphism testing for connected simple graphs, apart from $K_3$ and $K_{1,3}$, to be formulated as distinguishing their li...
By Fan Yang
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.
By Gyeongwon Jeong, Seonghun Park, Jihoon Hyun, Sang-il Oum, Hongseok Yang
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.
By Rui Wu, Zongyuan Chen, Hong Xie
arXiv:2604. 02995v3 Announce Type: replace-cross Abstract: We introduce the penalised Saito functional $\mathfrak S_{\lambda,\beta}(\mathcal{A};d_1,d_2)$ for a reduced arrangement $\mathcal{A}$ of $n$ lines and a prescribed pair $d_1+d_2=n-1$.
By Tom\'as S. R. Silva
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.
By Nathaniel Itty, Christopher D. Rosin, Chase Carstensen, Daniel Reichman
arXiv:2605.20434v2 Announce Type: replace-cross
Abstract: We study the contradiction graphs associated with a binary concept class. For a class $H\subseteq\{0,1\}^X$, the order-$m$ contradiction grap...
By Jesse Campbell, Daniel Ibaibarriaga, Lev Reyzin
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 $\Sigma_{\mathrm{HG}}$.
By Mario Pascual-Gonzalez, Ezequiel Lopez-Rubio
arXiv:2608. 08118v1 Announce Type: new Abstract: There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators.
By David Seka, Stefan Szeider
arXiv:2608. 10420v1 Announce Type: new Abstract: Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts.
By Xin Xu