{"id":"palomar/PALOMAR-2026-10-17-000005","url":"https://github.com/shaikidris/kkp-asymptotic-spectral-bound/tree/8aa258c7a0b06ae96cfa56018bddd60ee643efd5","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-17-000005-v1.json","repo":"https://github.com/shaikidris/kkp-asymptotic-spectral-bound","tags":["math.CO","msc:05C50","msc:05C35","spectral-graph-theory","forbidden-subgraphs","extremal-graph-theory"],"score":0,"title":"A sharp asymptotic spectral bound for forbidden subgraphs","trust":"high","domain":"math.CO","source":"palomar","authors":["Idris Ali Shaik"],"reviews":0,"subject":"math.CO","summary":"For every fixed finite graph F of chromatic number r+1 at least three and every positive epsilon, there is an edge threshold M such that every finite simple F-free graph G with m at least M satisfies F2(A_G) <= 2(1-1/r)m - (2(1-1/r)-1)Delta(G) + epsilon m. F2 is the sum of the squares of the two largest positive adjacency eigenvalues with missing terms padded by zero. The graphs may be disconnected. A companion theorem establishes agreement with the two largest ordered eigenvalue squares in the same eventual range. Enough edges force an F-free graph to be noncomplete; BN nonedge interlacing…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-17","reactions":{},"formalized":true,"formalizes":[{"title":"Asymptotic rank two spectral bounds and a color critical counterexample","identifier":"","relationship":"formalizes"}]}