graph theory

``` Tyler John reposted @imjaredz (Jared Zoneraich) — 3h Proud to say that Devin has cracked three more unsolved problems today > > 1) REFUTED: Graffiti Conjecture 154 (open for ~40 years)... > [same three-panel chart image as previous screenshot, showing Graffiti conjecture 154, Graffiti conjectures 39 & 40, and Brandt's regular-supergraph conjecture] ```

@tenobrus (Tenobrus) — 43m could not begin to tell you what the fuck Sol is getting up to here but it sure seems to be having fun doing it [Embedded code/diff screenshot, three file-creation blocks:] research_tasks/round1/solbbf_separators.md (+7 -0) 1 +Read `research_tasks/round1/COMMON.md`. Explore modular decomposition, 2 +clique sums, and small-separator gluing. Try to arrange two globally 3 +different gluings that become isomorphic after deleting vertices in a large 4 +fraction of pieces. Count exact repairable deletions, or prove a separator 5 +tax theorem bounding their density. Check that local piece isomorphisms are 6 +globally compatible after deletion. Write 7 +`research/agents/solbbf_separators/round1.md`. research_tasks/round1/solbbf_substitution.md (+7 -0) 1 +Read `research_tasks/round1/COMMON.md`. Develop graph substitution or 2 +lexicographic-composition formulas for vertex decks. Determine exactly how 3 +base deletions and module deletions contribute, including newly merged twin 4 +classes. Seek a composition that amplifies a finite positive-excess seed 5 +into an unbounded family, or prove a no-amplification theorem for a broad 6 +substitution class. Write 7 +`research/agents/solbbf_substitution/round1.md`. research_tasks/round1/solbbf_tree_unicyclic.md (+6 -0) 1 +Read `research_tasks/round1/COMMON.md`. Revisit tree/unicyclic and 2 +sunshine/caterpillar supercard mechanisms as a source of exact deletion 3 +symmetries. Generalize beyond the known family rather than reproving its 4 +published asymptotic bound. Derive exact common-card formulas and determine 5 +whether grafting or multi-cycle variants can reach the BBF slope. Write 6 +`research/agents/solbbf_tree_unicyclic/round1.md`.

@ChrisPainterYup (Chris Painter) — 3h The prompt: "You should do a breakthrough" [Embedded screenshot of a chat/agent interface:] Yesterday 2:29 AM 📁 Uploaded a file Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample. Worked for 52m 52s > > QUOTED: @DmitryRybin1 (Dmitry Rybin) — 12h > Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. > The graph below has fractional flo... [truncated, embedded graph-theory diagram image]