On contractible and vertically contractible elements in 3-connected matroids and graphs

Discrete Mathematics

Volumn 179, Issue 1-3, 1998, Pages 185-203

  Wu, Haidong ^a  

^a SOUTHERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042416978     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(96)00385-8     Document Type: Article

References (23)

1. S. Akkari and J.G. Oxley, Some local extremal connectivity results for matroids, Combin. Probab. Comput. 2 (1993) 367-384.
2. R.E.L. Aldred, R.L. Hemminger and K. Ota, The 3-connected graphs having a longest cycle containing only three contractible edges, J. Graph Theory 17 (1993) 361-371.
3. K. Ando, H. Enomoto and A. Saito, Contractible edges in 3-connected graphs, J. Combin. Theory Ser. B 42 (1987) 87-93.
4. R.E. Bixby, A simple theorem on 3-connectivity, Linear Algebra Appl. 45 (1982) 123-126.
5. J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London; North-Holland, New York, 1976).
6. T.H. Brylawski, Modular constructions for combinatorial geometries, Trans. Amer. Math. Soc. 203 (1975) 1-44.
7. W.H. Cunningham, On matroid connectivity, J. Combin. Theory Ser. B 30 (1981) 94-99.
8. N. Dean, R.L. Hemminger and K. Ota, Longest cycles in 3-connected graphs contain three contractible edges, J. Graph Theory 12 (1989) 17-21.
9. Y. Egawa, Y. Enomoto and A. Saito, Contractible edges in triangle-free graphs, Combinatorica 6 (1986) 269-274.
10. M. Lemos, On 3-connected matroids, Discrete Math. 73 (1989) 273-283.
11. J.W. Leo, Triads and triangles in 3-connected matroids, submitted.
12. J.G. Oxley, On matroid connectivity, Quart. J. Math. Oxford Ser. (2) 32 (1981) 193-208.
13. J.G. Oxley, On 3-connected matroids, Canad. J. Math. 33 (1981) 20-27.
14. J.G. Oxley, On a matroid generalization of graph connectivity, Math. Proc. Camb. Phil. Soc. 90 (1981) 207-214.
15. J.G. Oxley, Matroid Theory (Oxford Univ. Press, New York, 1992).
16. J.G. Oxley and H. Wu, On matroid connectivity, Discrete Math. 146 (1995) 321-324.
17. J.G. Oxley and H. Wu, On the structure of 3-connected matroids and graphs, submitted.
18. J.G. Oxley and H. Wu, Matroids and graphs with few non-essential elements, submitted.
19. P.D. Seymour, Decomposition of regular matroids, J. Combin. Theory Ser. B 28 (1980) 305-359.
20. C. Thomassen, Planarity and duality of finite and infinite graphs, J. Combin. Theory Ser. B 29 (1980) 244-271.
21. C. Thomassen and B. Toft, Non-separating induced cycles in graphs, J. Combin. Theory Ser. B 31 (1981) 199-224.
22. W.T. Tutte, A theory of 3-connected graphs, Nederl. Akad. Wetensch. Proc. Ser. A 64 (1961) 441-455.
23. W.T. Tutte, Connectivity in matroids, Canad. J. Math. 18 (1966) 1301-1324.