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 Km,n with m, n ≥ 5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs.
Keywords
Cycle space, Cycle basis, robust, quasi-robust, Kainen's Basis, elementary cycle, complete bipartite, Cartesian product
DOI: https://doi.org/10.26493/1855-3974.104.5b7
ISSN: 1855-3974
Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications