A note on fundamental, non-fundamental, and robust cycle bases

DOI10.1016/j.dam.2008.06.047zbMath1163.92002OpenAlexW2121314886WikidataQ56990840 ScholiaQ56990840MaRDI QIDQ1026213

Konstantin Klemm, Peter F. Stadler

Publication date: 24 June 2009

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2008.06.047

zbMATH Keywords

cycle basisfundamental cycle basiscyclically robust basis

Mathematics Subject Classification ID

Applications of graph theory (05C90) Paths and cycles (05C38) General biology and biomathematics (92B05)

Related Items (7)

A Family of Tree-Based Generators for Bubbles in Directed Graphs ⋮ A family of tree-based generators for bubbles in directed graphs ⋮ Graph bases and diagram commutativity ⋮ Robust cycle bases do not exist for \(K_{n, n}\) if \(n \geq 8\) ⋮ Canonical sphere bases for simplicial and cubical complexes ⋮ Classification of robust cycle bases and relations to fundamental cycle bases ⋮ Cyclic matrices of weighted digraphs

Cites Work

• Classes of cycle bases
• Cycle bases from orderings and coverings
• Characterizations of outerplanar graphs
• Is every cycle basis fundamental?
• An Efficient Cycle Vector Space Algorithm for Listing All Cycles of a Planar Graph
• An algorithm for the longest cycle problem
• On Vector Spaces Associated with a Graph
• On a problem of P. Erdös

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