arXiv AI
Edge-addition monotonicity of positive p-energy fails for every p >= 1
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Phase Transition for Stochastic Block Model with more than $\sqrt{n}$ Communities
arXiv:2509. 15822v3 Announce Type: replace-cross Abstract: Predictions from statistical physics postulate that recovery of the communities in the Stochastic Block Model (SBM) with a fixed number $K$ of communities is possible in polynomial time above, and only above, the Kesten-Stigum (KS) threshold.
arXiv AI
Jul 24
Improved lower bounds for the Shannon capacity of odd cycles
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 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 16
On the Expressive Power of Implicit Line-Graph Higher-Order Weisfeiler--Leman
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...
arXiv Machine Learning
Sep 15
Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification
arXiv:2609.10487v2 Announce Type: replace Abstract: We construct counterexamples to Rockafellar's sum conjecture in which two maximally monotone operators satisfy the interior-domain condition but th...