Demonstrates spanning subdivisions of cliques in pseudorandom graphs, suggesting implications for graph theory.
In this paper, we study the appearance of a spanning subdivision of a clique in graphs satisfying certain pseudorandom conditions. Specifically, we show the following results. (i) There are constants upper C greater than 0 C > 0 C> 0 and c element of left parenthesis 0 comma 1 right bracket c ∈ ( 0 , 1 ] c∈ (0,1] such that, whenever d divided by lamda greater than or equals upper C d / λ ≥ C d/λ ≥ C , every left parenthesis n comma d comma lamda right parenthesis ( n , d , λ ) (n,d,λ ) -graph contains a spanning subdivision of upper K Subscript t K t Kₜ for all 2 less than or equals t less than or equals min left brace c d comma c StartRoot StartFraction n Over log n EndFraction EndRoot right brace 2 ≤ t ≤ min { c d , c n log n } 2≤ t ≤ min ,c√n/log n\ . (ii) There are constants
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Pavez‐Signé et al. (2026) studied this question.
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