On the Structure of 3-connected Matroids and Graphs

European Journal of Combinatorics

Volumn 21, Issue 5, 2000, Pages 667-688

  Oxley, James ^a   Wu, Haidong ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034393571     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1006/eujc.2000.0407     Document Type: Article

References (33)

1. S. Akkari, A minimal 3-connectedness result for matroids, Discrete Math., 103 (1992), 221-232.
2. S. Akkari and J. Oxley, Some extremal connectivity results for matroids, J. Comb. Theory, Ser. B, 52 (1991), 301-320.
3. S. Akkari and J. Oxley, Some local extremal connectivity results for matroids, Comb. Probab. Comput., 2 (1993), 367-384.
4. R. E. Bixby, A simple theorem on 3-connectivity, Linear Algebra Appl., 45 (1982), 123-126.
5. R. E. Bixby and C. R. Coullard, On chains of 3-connected matroids, Discrete Appl. Math., 15 (1986), 155-166.
6. R. E. Bixby and C. R. Coullard, Finding a smallest 3-connected minor maintaining a fixed minor and a fixed element, Combinatorica, 7 (1987), 231-242.
7. T. H. Brylawski, A combinatorial model for series-parallel networks, Trans. Am. Math. Soc., 154 (1971), 1-22.
8. T. H. Brylawski, Modular constructions for combinatorial geometries, Trans. Am. Math. Soc., 203 (1975), 1-44.
9. C. R. Coullard, L. L. Gardner and D. K. Wagner, Decomposition of 3-connected graphs, Combinatorica, 13 (1993), 7-30.
10. C. R. Coullard and J. G. Oxley, Extensions of Tutte's wheels-and-whirls theorem, J. Comb. Theory, Ser. B, 56 (1992), 130-140.
11. W. H. Cunningham, On matroid connectivity, J. Comb. Theory, Ser. B, 30 (1981), 94-99.
12. B. S. Gubser, Planar graphs with no 6-wheel minor, Discrete Math., 120 (1993), 59-73.
13. M. Lemos, On 3-connected matroids, Discrete Math., 73 (1989), 273-283.
14. S. Negami, A characterization of 3-connected graphs containing a given graph, J. Comb. Theory, Ser. B, 32 (1982), 69-74.
15. J. G. Oxley, On matroid connectivity, Q. J. Math. Oxford Ser. (2), 32 (1981), 193-208.
16. J. G. Oxley, On 3-connected matroids, Can. J. Math., 33 (1981), 20-27.
17. J. G. Oxley, On nonbinary 3-connected matroids, Trans. Am. Math. Soc., 300 (1987), 663-679.
18. J. G. Oxley, The binary matroids with no 4-wheel minor, Trans. Am. Math. Soc., 301 (1987), 63-75.
19. 4)-minor, J. Comb. Theory, Ser. B, 42 (1987), 212-249.
20. J. G. Oxley, The regular matroids with no 5-wheel minor, J. Comb. Theory, Ser. B, 46 (1989), 292-305.
21. J. G. Oxley, Matroid Theory, Oxford University Press, New York, 1992.
22. J. G. Oxley and T. J. Reid, The smallest rounded sets of binary matroids, Europ. J. Combinatorics, 11 (1990), 47-56.
23. J. G. Oxley and H. Wu, A note on matroid connectivity, Discrete Math., 146 (1995), 321-324.
24. J. G. Oxley and H. Wu, Matroids and graphs with few non-essential elements, Graphs Combin., to appear.
25. N. Robertson and P. D. Seymour, Generalizing Kuratowski's theorem, Congressus Numerantium, 45 (1984), 129-138.
26. P. D. Seymour, Decomposition of regular matroids, J. Comb. Theory, Ser. B, 28 (1980), 305-359.
27. P. D. Seymour, Matroid minors, in: Handbook of Combinatorics, R. Graham, M. Grötschel and L. Lovász (eds), Elsevier, Amsterdam, 1995, pp. 527-550.
28. J. J.-M. Tan, Matroid 3-connectivity, Ph. D. Thesis, Carleton University, 1981.
29. K. Truemper, Partial matroid representations, Europ. J. Combinatorics, 5 (1984), 377-394.
30. K. Truemper, Matroid Decomposition, Academic Press, New York, 1992.
31. W. T. Tutte, A theory of 3-connected graphs, Nederl. Akad. Wetensch. Proc. Ser. A, 64 (1961), 441-455.
32. W. T. Tutte, Connectivity in matroids, Can. J. Math., 18 (1966), 1301-1324.
33. H. Wu, On contractible and vertically contractible elements in 3-connected matroids and graphs, Discrete Math., 179 (1998), 185-203.