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On the connectivity of extremal Ramsey graphs

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Beveridge, Andrew and Pikhurko, Oleg (2008) On the connectivity of extremal Ramsey graphs. Australasian Journal of Combinatorics, Vol.41 . pp. 57-61.

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Official URL: http://ajc.maths.uq.edu.au/pdf/41/ajc_v41_p057.pdf

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Abstract

An (r, b)-graph is a graph that contains no clique of size r and no independent set of size b. The set of extremal Ramsey graphs ERG(r, b) consists of all (r, b)-graphs with R(r, b) − 1 vertices, where R(r, b) is the classical Ramsey number. We show that any G ∈ ERG(r, b) is r − 1 vertex connected and 2r − 4 edge connected for r, b ≥ 3.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Australasian Journal of Combinatorics
Publisher: Centre for Discrete Mathematics & Computing
ISSN: 1034-4942
Official Date: 2008
Dates:
DateEvent
2008Published
Volume: Vol.41
Number of Pages: 5
Page Range: pp. 57-61
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
Funder: National Science Foundation
Grant number: DMS-0457512
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