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

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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

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80Endgültige, publizierte Fassung, 210 KBLizenz: CC BY

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

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AU - Stadler, Peter F.

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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.

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JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

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