Edge-disjoint odd cycles in planar graphs

Journal of Combinatorial Theory. Series B

Volumn 90, Issue 1, 2004, Pages 107-120

  Král, Daniel ^a   Voss, Heinz Jürgen ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Bipartite graphs; Erd s P a property; Odd cycles; Planar graphs

Indexed keywords

EID: 0347129762     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0095-8956(03)00078-9     Document Type: Article

References (20)

1. S. Brandt, Lösung zu Problem 66, in: Mathematische Semesterberichte, Vol. 44, Springer, Berlin, 1997, pp. 95-96.
2. C. Berge, B. Reed, Optimal packings of edge-disjoint odd cycles, Discrete Math. 211 (2000) 197-202.
3. W.J. Cook, W.H. Cunningham, W.R. Pulleyblank, A. Schrijver, Combinatorial Optimization, Wiley Interscience Series in Discrete Mathematics and Optimization, Wiley, New York, 1998.
4. P. Erdos, L. Pósa, On independent circuits contained in a graph, Canad. J. Math. 17 (1965) 347-352.
5. P. Festa, P.M. Pardalos, M.G.C. Resende, Feedback set problems, in: D.Z. Du, P.M. Pardalos (Eds.), Handbook of Combinatorial Optimization, Vol. 4, Kluwer Academic Publishers, Dordrecht, 1999, pp. 209-258.
6. F.O. Hadlock, Finding a maximum cut of a planar graph in polynomial time, SIAM J. Comput. 4 (1975) 221-225.
7. M. Krivelevich, On a conjecture of Tuza about packing and covering of triangles, Discrete Math. 142 (1995) 281-286.
8. D. Rautenbach, B. Reed, The Erdos-Pósa property for odd cycles in highly connected graphs, Combinatorica 21 (2001) 267-278.
9. B. Reed, Mangoes, blueberries, Combinatorica, 19 (2) (1999) 267-296.
10. N. Robertson, D.P. Sanders, P.D. Seymour, R. Thomas, The four-colour theorem, J. Combin. Theory, Ser. B 70 (1999) 2-44.
11. A. Schrijver, Theory of Linear and Integer Programming, Wiley, Chichester, 1986.
12. P.D. Seymour, On odd cuts and plane multicommodity flows, Proc. London Math. Soc. (1981), 178-192.
13. H. Simonovits, A new proof and generalizations of a theorem of Erdos and Pósa on graphs without k + 1 independent circuits, Acta Math. Acad. Sci. Hung. 18 (1967) 191-206.
14. C. Thomassen, The Erdos-Pósa property for odd cycles in graphs of large connectivity, MAT-report no. 1999-08, Technical University of Denmark.
15. Z. Tuza, A conjecture on triangles of graphs, Graphs Combin. 6 (1990) 373-380.
16. H.-J. Voss, Some properties of graphs containing k independent circuits, in: Proceedings of the Coll. Tihany, Publ. House Hung. Acad. Sci., Budapest, 1966, Academic Press, New York, 1968, pp. 321-334.
17. H.-J. Voss, in: Cycles and bridges in graphs, Mathematics and its Applications, East European Series, Vol. 49, Kluwer Academic Publishers, Dordrecht, 1991.
18. H.J. Voss, H. Walther, Über Kreise in Graphen (in German), Deutscher Verlag der Wissenschaften, 1972.
19. D. West (Ed.), Open Problems Column #14 of SIAM Activity Group Newsletter in Discrete Mathematics, Spring 1994.
20. M. Yannakakis, Node and edge-deletion NP-compiete problems, in: Proceedings of the 10th Annual ACM Symposium on Theory of Computing, San Diego, California, 1978, pp. 296-313.