Tiling randomly perturbed multipartite graphs
Year: 2025
Type: preprint
Abstract: A perfect $K_r$-tiling in a graph $G$ is a collection of vertex-disjoint copies of the graph $K_r$ in $G$ that covers all vertices of $G$. In this paper, we prove that the threshold for the existence of a perfect $K_{r}$-tiling of a randomly perturbed balanced $r$-partite graph on $rn$ vertices is $n^{-2/r}$. This result is a multipartite analog of a theorem of Balogh, Treglown, and Wagner and extends our previous result, which was limited to the bipartite setting.
Source: arXiv (Cornell University)
Authors: Gomez-Leos, Enrique, Martin, Ryan R.
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6910695560
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