A note on quasi-robust cycle bases

Philipp-Jens Ostermeier; Marc Hellmuth; Konstantin Klemm; Josef Leydold; Peter F. Stadler

A note on quasi-robust cycle bases

Philipp-Jens Ostermeier, Marc Hellmuth, Konstantin Klemm, Josef Leydold, Peter F. Stadler

Publikation: Wissenschaftliche Fachzeitschrift › Originalbeitrag in Fachzeitschrift › Begutachtung

20 Downloads (Pure)

Abstract

We investigate here some aspects of cycle bases of undirected graphs that allow the iterative construction of all elementary cycles. We introduce the concept of quasi-robust bases as a generalization of the notion of robust bases and demonstrate that a certain class of bases of the complete bipartite graphs K m,n with m,n ≥5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs.

Originalsprache	Englisch
Seiten (von - bis)	213 - 240
Fachzeitschrift	Ars Mathematica Contemporanea
Jahrgang	2
Publikationsstatus	Veröffentlicht - 1 Aug. 2009

Zugriff auf Dokument

80Endgültige, publizierte Fassung, 210 KBLizenz: CC BY

Verfügbarkeit prüfen

Katalog der Universitätsbibliothek

Andere Dateien und Links

http://amc.imfm.si/index.php/amc/article/viewFile/104/80

Zitat

@article{db31f191052047f68ba15b22eedeaeee,

title = "A note on quasi-robust cycle bases",

abstract = "We investigate here some aspects of cycle bases of undirected graphs that allow the iterative construction of all elementary cycles. We introduce the concept of quasi-robust bases as a generalization of the notion of robust bases and demonstrate that a certain class of bases of the complete bipartite graphs K m,n with m,n ≥5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs.",

author = "Philipp-Jens Ostermeier and Marc Hellmuth and Konstantin Klemm and Josef Leydold and Stadler, {Peter F.}",

year = "2009",

month = aug,

day = "1",

language = "English",

volume = "2",

pages = "213 -- 240",

journal = "Ars Mathematica Contemporanea",

issn = "1855-3966",

publisher = "Society of Mathematicians, Physicists and Astronomers of Slovenia",

}

TY - JOUR

T1 - A note on quasi-robust cycle bases

AU - Ostermeier, Philipp-Jens

AU - Hellmuth, Marc

AU - Klemm, Konstantin

AU - Leydold, Josef

AU - Stadler, Peter F.

PY - 2009/8/1

Y1 - 2009/8/1

N2 - We investigate here some aspects of cycle bases of undirected graphs that allow the iterative construction of all elementary cycles. We introduce the concept of quasi-robust bases as a generalization of the notion of robust bases and demonstrate that a certain class of bases of the complete bipartite graphs K m,n with m,n ≥5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs.

AB - We investigate here some aspects of cycle bases of undirected graphs that allow the iterative construction of all elementary cycles. We introduce the concept of quasi-robust bases as a generalization of the notion of robust bases and demonstrate that a certain class of bases of the complete bipartite graphs K m,n with m,n ≥5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs.

UR - http://amc.imfm.si/index.php/amc/article/viewFile/104/80

M3 - Journal article

SN - 1855-3966

VL - 2

SP - 213

EP - 240

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

ER -