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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2013 Volume 417, Pages 11–85 (Mi znsl5709)

Generalized flowers in $k$-connected graph. Part 2

A. L. Glazmanab

a St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
b Section de Mathématiques, Université de Genève. 2-4 rue du Lièvre, Case postale 64, 1211 Genève, Suisse

Abstract: We continue the work started in [8] and research $k$-cutsets in $k$-connected graphs. Several new statesments concerning the structure of generalized flowers in $k$-connected graphs are proved here. Generalized flowers in the case $k=4$ are considered after. For $k=4$ we give the description of maximal generalized flowers with an empty center which have a common catset.

Key words and phrases: $k$-connected graph, $4$-connected graph, cutset.

UDC: 519.173.1

Received: 05.11.2013


 English version:
Journal of Mathematical Sciences (New York), 2015, 204:2, 185–231

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© Steklov Math. Inst. of RAS, 2024