arXiv AI
On the Expressive Power of Implicit Line-Graph Higher-Order Weisfeiler--Leman
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arXiv AI
Aug 13
A Forced-Structure Reduction and Verifiable Bounds for Conway's 99-Graph
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.
arXiv AI
Jul 28
Formalizing Flag Algebras in Lean
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 AI
Sep 4
AutoGraphForge: Towards Automated Graph Theory Discovery
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.
arXiv AI
Sep 15
Edge-addition monotonicity of positive p-energy fails for every p >= 1
arXiv:2609.13476v1 Announce Type: cross Abstract: At a 2021 AIM workshop, Guo conjectured that the positive square energy s+ = E+_2 should inherit the familiar edge-addition monotonicity of the spect...
arXiv Machine Learning
Sep 10
Expressivity of Contradiction Graphs
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...
arXiv AI
Jul 14
Instruction Set and Language for Hypergraphs
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 $\Sigma_{\mathrm{HG}}$.