Abstract: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 three results. Firstly, that there are constants $C>0$ and $c\in (0,1]$ such that, whenever $d/\lambda\ge C$, every $(n,d,\lambda)$-graph contains a spanning subdivision of $K_t$ for all $2\le t \le \min\{cd,c\sqrt{\frac{n}{\log n}}\}$. Secondly, that there are constants $C>0$ and $c\in (0,1]$ such that, whenever $d/\lambda\ge C\log^3n$, every $(n,d,\lambda)$-graph contains a spanning nearly-balanced subdivision of $K_t$ for all $2\le t \le \min\{cd,c\sqrt{\frac{n}{\log^3n}}\}$. Finally, we show that for every $\mu>0$, there are constants $c,\varepsilon\in (0,1]$ and $n_0\in \mathbb N$ such that, whenever $n\ge n_0$, every $n$-vertex graph with minimum degree at least $\mu n$ and no bipartite holes of size $\varepsilon n$ contains a spanning nearly-balanced subdivision of $K_t$ for all $2\le t \le c\sqrt{n}$.
From: Teo Petrov [view email]
[v1]
Wed, 2 Apr 2025 11:46:24 UTC (26 KB)
[v2]
Mon, 6 Jul 2026 07:23:26 UTC (25 KB)
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