Cycle bases in graphs characterization, algorithms, complexity, and applications

@article{Kavitha2009CycleBI,
  title={Cycle bases in graphs characterization, algorithms, complexity, and applications},
  author={T. Kavitha and Christian Liebchen and K. Mehlhorn and D. Michail and R. Rizzi and T. Ueckerdt and K. Zweig},
  journal={Comput. Sci. Rev.},
  year={2009},
  volume={3},
  pages={199-243}
}
Cycles in graphs play an important role in many applications, e.g., analysis of electrical networks, analysis of chemical and biological pathways, periodic scheduling, and graph drawing. From a mathematical point of view, cycles in graphs have a rich structure. Cycle bases are a compact description of the set of all cycles of a graph. In this paper, we survey the state of knowledge on cycle bases and also derive some new results. We introduce different kinds of cycle bases, characterize them in… Expand
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References

SHOWING 1-10 OF 93 REFERENCES
New Approximation Algorithms for Minimum Cycle Bases of Graphs
On finding cycle bases and fundamental cycle bases with a shortest maximal cycle
  • G. Galbiati
  • Mathematics, Computer Science
  • Inf. Process. Lett.
  • 2003
Union of all the Minimum Cycle Bases of a Graph
  • P. Vismara
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 1997
Algorithms for Generating Fundamental Cycles in a Graph
A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs
A Faster Algorithm for Minimum Cycle Basis of Graphs
Minimum Cycle Bases for Network Graphs
Classes of cycle bases
An improved heuristic for computing short integral cycle bases
Minimum cycle bases: Faster and simpler
...
1
2
3
4
5
...