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- W4287688724 abstract "One interesting question is how a graph develops from some constrained random graph process, which is a fundamental mechanism in the formation and evolution of dynamic networks. The problem here is referred to the random $K_k$-removal algorithm. For a fixed integer $kgeqslant 3$, it starts with a complete graph on $nrightarrowinfty$ vertices and iteratively removes the edges of an uniformly chosen $K_k$. This algorithm terminates once no $K_k$s remain and at the same time it generates one linear $k$-uniform hypergraph. For $k=3$, it was shown that the size in the final graph is $n^{3/2+o(1)}$. Less results are on the cases when $kgeqslant 4$. In this paper, we prove that the exact expected trajectories of various key parameters in the algorithm to some iteration such that the final size in the algorithm is at most $n^{2-1/(k(k-1)-2)+o(1)}$ for $kgeqslant 4$. We also show the bound is a natural barrier." @default.
- W4287688724 created "2022-07-26" @default.
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- W4287688724 date "2020-08-16" @default.
- W4287688724 modified "2023-10-13" @default.
- W4287688724 title "Random $K_k$-removal algorithm" @default.
- W4287688724 doi "https://doi.org/10.48550/arxiv.2008.06839" @default.
- W4287688724 hasPublicationYear "2020" @default.
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