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The $Q_2$-Free Process in the Hypercube

dc.contributor.authorJohnson, JR
dc.contributor.authorPinto, T
dc.date.accessioned2020-12-07T11:55:21Z
dc.date.available2020-10-04
dc.date.available2020-12-07T11:55:21Z
dc.date.issued2020-11-13
dc.identifier.urihttps://qmro.qmul.ac.uk/xmlui/handle/123456789/69082
dc.description.abstractThe generation of a random triangle-saturated graph via the triangle-free process has been studied extensively. In this short note our aim is to introduce an analogous process in the hypercube. Specifically, we consider the Q 2 -free process in Q d and the random subgraph of Q d it generates. Our main result is that with high probability the graph resulting from this process has at least c d 2 / 3 2 d edges. We also discuss a heuristic argument based on the differential equations method which suggests a stronger conjecture, and discuss the issues with making this rigorous. We conclude with some open questions related to this process.en_US
dc.publisherThe Electronic Journal of Combinatoricsen_US
dc.relation.ispartofThe Electronic Journal of Combinatorics
dc.rightsThis article is distributed under the terms of the CC-BY-NC License.
dc.rightsAttribution-NonCommercial 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/3.0/us/*
dc.titleThe $Q_2$-Free Process in the Hypercubeen_US
dc.typeArticleen_US
dc.rights.holder© 2020, The Author(s)
dc.identifier.doi10.37236/8864
pubs.issue4en_US
pubs.notesNot knownen_US
pubs.publication-statusPublisheden_US
pubs.volume27en_US
dcterms.dateAccepted2020-10-04
rioxxterms.funderDefault funderen_US
rioxxterms.identifier.projectDefault projecten_US


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