Interchangeability of relevant cycles in graphs

Electronic Journal of Combinatorics

Volumn 7, Issue 1 R, 2000, Pages 1-16

  Gleiss, Petra M ^a   Leydold, Josef ^b   Stadler, Peter F ^a,c  

^a UNIVERSITY OF VIENNA   (Austria)

^b VIENNA UNIVERSITY OF ECONOMICS AND BUSINESS   (Austria)

^c SANTA FE INSTITUTE   (United States)

Author keywords

Minimum cycle basis; Relevant cycles

Indexed keywords

EID: 1842780616     PISSN: 10778926     EISSN: None     Source Type: Journal    
DOI: 10.37236/1494     Document Type: Article

References (18)

1. W.-K. Chen. On vector spaces associated with a graph. SIAM J. Appl. Math., 20:525-529, 1971.
2. D. M. Chickering, D. Geiger, and D. Heckerman. On finding a cycle basis with a shortest maximal cycle. Inform. Processing Let., 54:55-58, 1994.
3. L. O. Chua and L. Chen. On optimally sparse cycle and coboundary basis for a linear graph. IEEE Trans. Circuit Theory, 20:54-76, 1973.
4. G. A. Dirac. On rigid circuit graphs. Abh. Math. Sem. Hamburg, 25:71-76, 1961.
5. G. M. Downs, V. J. Gillet, J. D. Holliday, and M. F. Lynch. Review of ring perception algorithms for chemical graphs. J. Chem. Inf. Comput. Sci., 29:172-187, 1989.
6. P. M. Gleiss and P. F. Stadler. Relevant cycles in biopolymers and random graphs. Presented at the Fourth Slovene International Conference in Graph Theory, Bled, Slovenia, 1999.
7. D. Hartvigsen and R. Mardon. The all-pair min-cut problem and the minimum cycle basis problem on planar graphs. SIAM J. Discr. Math., 7:403-418, 1994.
8. J. D. Horton. A polynomial-time algorithm to find the shortest cycle basis of a graph. SIAM J. Comput., 16:359-366, 1987.
9. A. Kaveh. Structural Mechanics: Graph and Matrix Methods. Research Studies Press, Exeter, UK, 1992.
10. J. Leydold and P. F. Stadler. Minimal cycle basis of outerplanar graphs. Electr. J. Comb., 5:R16, 1998. See http://www.combinatorics.org.
11. J. Oxley. Graphs and series-parallel networks. In N. White, editor, Theory of Matroids, volume 26 of Encyclopedia of Mathematics and Applications, pages 97-126. Cambridge University Press, Cambridge, UK, 1986.
12. M. Plotkin. Mathematical basis of ring-finding algorithms in CIDS. J. Chem. Doc., 11:60-63, 1971.
13. P. F. Stadler and C. Haslinger. RNA structures with pseudo-knots: Graph-theoretical and combinatorial properties. Bull. Math. Biol., 61:437-467, 1999.
14. C. Thomassen. Embeddings and minors. In R. Graham, M. Gr̈otschel, and L. Lovász, editors, Handbook of Combinatorics, pages 301-349. North-Holland, Amsterdam, 1995.
15. P. Vismara. Union of all the minimum cycle bases of a graph. Electr. J. Comb., 4:73-87, 1997. Paper No. #R9 (15 pages).
16. A. E. Walter, D. H. Turner, J. Kim, M. H. Lyttle, P. M̈uller, D. H. Mathews, and M. Zuker. Co-axial stacking of helixes enhances binding of oligoribonucleotides and improves predicions of RNA folding. Proc. Natl. Acad. Sci. USA, 91:9218-9222, 1994.
17. M. S. Waterman. Secondary structure of single-stranded nucleic acids. Adv. Math. Suppl. Studies, 1:167-212, 1978.
18. D. J. A. Welsh. Matroids: Fundamental concepts. In R. Graham, M. Gr̈otschel, and L. Lovász, editors, Handbook of Combinatorics, pages 483-526. North-Holland, Amsterdam, 1995.