{"id":"palomar/PALOMAR-2026-10-29-000023","url":"https://github.com/jtraverso/shannon-edge-colouring/tree/d590cfeb50d88710b454905f896aab928fcb5156","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-29-000023-v1.json","repo":"https://github.com/jtraverso/shannon-edge-colouring","tags":["math.CO","msc:05C15"],"score":0,"title":"Shannon's theorem on edge colourings of multigraphs","trust":"high","domain":"math.CO","source":"palomar","authors":["Juan Pablo Traverso Gianini"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 / Mathlib formalization of Shannon's theorem (1949): every finite loopless multigraph of maximum degree at most Δ has a proper edge colouring with ⌊3Δ/2⌋ colours; and its sharpness: for every Δ the Shannon triangle (three vertices with ⌊Δ/2⌋, ⌊Δ/2⌋ and ⌈Δ/2⌉ parallel edges between the three pairs) has maximum degree at most Δ and no proper edge colouring with fewer than ⌊3Δ/2⌋ colours. Multigraphs are edge families ends : ι → V × V (parallel edges allowed), a lighter representation than Mathlib's multigraph structure Graph α β (Mathlib.Combinatorics.Graph.Basic: vertex and edge sets…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-29","reactions":{},"formalized":true,"formalizes":[{"title":"A theorem on coloring the lines of a network","identifier":"doi:10.1002/sapm1949281148","relationship":"formalizes"}]}