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.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.
arXiv:2608. 30273v1 Announce Type: cross Abstract: The exact Shannon capacity is unknown for every odd cycle beyond the five-cycle $C_5$, making odd cycles a central open problem in zero-error information theory.
arXiv:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.
We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity.
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:2609. 02659v1 Announce Type: cross Abstract: The pairwise independent correlation gap is the ratio of the maximum expected value of a set function under arbitrary dependence to that under pairwise independence, measuring the loss from this independence restriction.
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...