Classification of robust cycle bases and relations to fundamental cycle bases
نویسندگان
چکیده
منابع مشابه
A note on fundamental, non-fundamental, and robust cycle bases
In many biological systems, robustness is achieved by redundant wiring, and reflected by the presence of cycles in the graphs connecting the systems’ components. When analyzing such graphs, cyclically robust cycle bases of are of interest since they can be used to generate all cycles of a given 2-connected graph by iteratively adding basis cycles. It is known that strictly fundamental (or Kirch...
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Two types of robust cycle bases are defined via recursively nice arrangements; complete and bipartite complete graphs are shown to have such bases. It is shown that a diagram in a groupoid is commutative up to natural equivalence (cutne) if for each cycle in a robust basis of the graph underlying the diagram, the composition of the morphisms is naturally equivalent to the identity. For a hyperc...
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An undirected biconnected graph G with nonnegative integer lengths on the edges is given. The problem we consider is that of finding a cycle basis B of G such that the length of the longest cycle included in B is the smallest among all cycle bases of G. We first observe that Horton’s algorithm [SIAM J. Comput. 16 (2) (1987) 358–366] provides a fast solution of the problem that extends the one g...
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ژورنال
عنوان ژورنال: The Art of Discrete and Applied Mathematics
سال: 2017
ISSN: 2590-9770
DOI: 10.26493/2590-9770.1218.dac