Open access
Date
2023Type
- Conference Paper
ETH Bibliography
yes
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Abstract
In [13], Kahn gave the strongest possible, affirmative, answer to Shamir’s prob-lem, which had been open since the late 1970s: Letr>3and letnbe divisible byr. Then, in the randomr-uniform hypergraph process onnvertices, as soon as thelast isolated vertex disappears, a perfect matching emerges. In the present work, weprove the analogue of this result for clique factors in the random graph process: Atthe time that the last vertex joins a copy of the complete graphKr, the random graphprocess contains aKr-factor. Our proof draws on a novel sequence of couplings whichembeds the random hypergraph process into the cliques of the random graph process.An analogous result is proved for clique factors in thes-uniform hypergraph process(s>3). Show more
Permanent link
https://doi.org/10.3929/ethz-b-000654076Publication status
publishedExternal links
Book title
Proceedings of the 12th European Conference on Combinatorics, Graph Theory and ApplicationsPages / Article No.
Publisher
Masaryk UniversityEvent
Organisational unit
03672 - Steger, Angelika / Steger, Angelika
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ETH Bibliography
yes
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