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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Minimal braces

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Author(s):
Fabres, Phelipe A. [1] ; Kothari, Nishad [2] ; de Carvalho, Marcelo H. [1]
Total Authors: 3
Affiliation:
[1] FACOM UFMS, Campo Grande, MS - Brazil
[2] IC UNICAMP, BR-13083852 Campinas - Brazil
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL OF GRAPH THEORY; v. 96, n. 4, p. 490-509, MAR 2021.
Web of Science Citations: 0
Abstract

McCuaig proved a generation theorem for braces, and used it as the principal induction tool to obtain a structural characterization of Pfaffian braces. A brace isminimalif deleting any edge results in a graph that is not a brace. From McCuaig's brace generation theorem, we derive our main theorem that may be viewed as an induction tool for minimal braces. As an application, we prove that a minimal brace of order2nhas size at most5n-10, whenn >= 6, and we provide a complete characterization of minimal braces that meet this upper bound. A similar work has already been done in the context of minimal bricks by Norine and Thomas wherein they deduce the main result from the brick generation theorem due to the same authors. (AU)

FAPESP's process: 18/04679-1 - Conformal minors and Pfaffian orientations
Grantee:Nishad Bharat Kothari
Support Opportunities: Scholarships in Brazil - Post-Doctoral