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A note on quasi-robust cycle bases

: Ostermeier, P.-J.; Hellmuth, M.; Klemm, K.; Leydold, J.; Stadler, P.F.

Ars mathematica contemporanea 2 (2009), No.2, pp.231-240
ISSN: 1855-3966
ISSN: 1855-3974
Journal Article
Fraunhofer IZI ()

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.