Graph Sandwich Conjecture Resolved
Mathematicians have completed a decades-old proof showing that large random regular graphs can be rigorously “sandwiched” between two simpler random binomial graphs. The result, detailed on 18 September, lets researchers transfer many known properties of easy-to-analyze binomial graphs directly onto the harder regular graphs that better model real networks. It stands out because it unifies two long-studied random processes and immediately yields new theorems without case-by-case proofs.
Random binomial graphs, introduced in the 1950s, connect vertices by independent coin flips and are relatively tractable. Regular graphs, in which every vertex has the same degree, more accurately represent telephone networks, the internet or neural connections, yet their constrained edges make analysis far more difficult. In 2004 Jeong Han Kim and Van Vu conjectured that a suitable sandwich always exists for sufficiently large graphs; partial results accumulated over two decades until Richard Montgomery, Natalie Behague and Daniel Iľkovič finished the proof in 2025 by constructing the graphs edge-by-edge with carefully weighted random choices.
The main uncertainty is how far the new techniques extend. Researchers already speak of multi-layer sandwiches and other graph families, but the practical reach for concrete network problems remains open. The methods enrich the combinatorial toolbox, yet their computational cost for very large instances is still untested.
Sources: Quanta Magazine.
Roman Space Telescope Fuel Life Doubled
NASA announced that the newly launched Nancy Grace Roman Space Telescope now carries enough propellant for at least 22 years of science operations—more than double the original 10-year design life. The extension, confirmed 18 September, stems from an exceptionally accurate first mid-course correction, extra fuel loaded at launch, and projected savings on remaining burns. The observatory is still en route to its L2 halo orbit and is expected to begin full operations after arrival in early December.
Roman launched on 30 August aboard a Falcon Heavy. Its first trajectory burn on 31 August used only 18 kg of hydrazine instead of the budgeted 200 kg and achieved >99 % accuracy. Because the spacecraft was lighter than the conservative mass limit used for planning, tanks were filled to capacity, adding further margin. Station-keeping once on orbit will require only modest burns every 28 days.
Key uncertainties remain hardware longevity, instrument performance and future funding rather than propellant. The 22-year figure is a fuel-limited potential, not a guaranteed lifetime; other systems could fail earlier. The mission is designed for possible in-space refueling, but that capability is not yet required.
Sources: ScienceDaily, NASA.
Ultrafast All-Optical Light Steering Chip
Caltech researchers demonstrated a silicon metasurface that redirects a light beam by up to 13 degrees in 74 femtoseconds—roughly the time light takes to cross a human hair—using only another light pulse. Highlighted 18 September, the device relies on the optical Kerr effect amplified by nanoscale pillars and opens paths to faster photonic computing, communications and sensing without electronic bottlenecks.
Conventional modulators rely on electronic excitation and relaxation, limiting speeds to nanoseconds or picoseconds. The new approach uses a patterned pump beam to induce an instantaneous refractive-index change in a high-Q amorphous-silicon metasurface; a probe beam then deflects according to that pattern. The observed speed matches the pump-pulse duration, indicating the material response itself may be even faster.
Open questions include scaling the deflection angle, efficiency under continuous operation, and integration into practical photonic circuits. The current limit is the laser pulse length rather than the metasurface; shorter pulses could push performance further, but thermal and fabrication constraints for large arrays remain unexplored.
Sources: ScienceDaily, Caltech, Nature Nanotechnology.