Geodesic
A note on quasi-robust cycle bases
Ars Mathematica Contemporanea, Tome 2 (2009) no. 2, pp. 231-240.

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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 Km,n with m, n ≥ 5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs.
DOI : 10.26493/1855-3974.104.5b7
Keywords: Cycle space, Cycle basis, robust, quasi-robust, Kainen's Basis, elementary cycle, complete bipartite, Cartesian product 
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Philipp-Jens Ostermeier; Marc Hellmuth; Josef Leydold; Konstantin Klemm; Peter F. Stadler. A note on quasi-robust cycle bases. Ars Mathematica Contemporanea, Tome 2 (2009) no. 2, pp. 231-240. doi : 10.26493/1855-3974.104.5b7. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.104.5b7/

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