Abstract
We prove Edmonds-Gallai type structure theorems for Mader’s edge- and vertex-disjoint paths including also capacitated variants, and state a conjecture generalizing Mader’s minimax theorems on path packings and Cunningham and Geelen’s path-matching theorem.
Supported by European MCRTN Adonet, Contract Grant No. 504438.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cornuéjols, G., Hartvigsen, D., Pulleyblank, D.: Packing subgraphs in a graph. Oper. Res. Letter 1/4, 139–143 (1981/1982)
Cunningham, W.H.: Matching, matroids and extensions. Math. Program. Ser. B 91/3, 515–542 (2002)
Cunningham, W.H., Geelen, J.F.: The optimal path–matching problem. Combinatorica 17/3, 315–336 (1997)
Edmonds, J.R.: Maximum matching and a polyhedron with 0,1-vertices. J. Res. Nat. Bur. Standards Sect. B, 125–130 (1968)
Edmonds, J.R., Johnson, E.L.: Matching: a well-solved class of integer linear programs. In: Guy, H., Sauer, S. (eds.) Combinatorial Structures and Their Applications, Calgary, Alberta (1969)
Frank, A., Szegõ, L.: A Note on the Path-Matching Formula. J. of Graph Theory 41/2, 110–119 (2002)
Gallai, T.: Neuer Beweis eines Tutte’schen Satzes. Magyar Tud. Akad. Mat. Kutató Int. Közl. 8, 135–139 (1963)
Gallai, T.: Maximale Systeme unabhänginger Kanten. Magyar Tud. Akad. Mat. Kutató Int. Közl. 9, 401–413 (1965)
Lovász, L.: On the structure of factorizable graphs. Acta Math. Acad. Sci. Hungar. 23, 179–195 (1972)
Lovász, L.: The factorization of graphs II. Acta Math. Acad. Sci. Hungar. 23, 223–246 (1972)
Lovász, L., Plummer, M.D.: Matching Theory. Akadémiai Kiadó, Budapest (1986)
Mader, W.: Über die Maximalzahl kantendisjunkter A-Wege. Arch. Math (Basel) 30/3, 325–336 (1978)
Mader, W.: Über die Maximalzahl kreuzungsfreier H-Wege. Archiv der Mathematik (Basel) 31, 387–402 (1978)
Schrijver, A.: A short proof of Mader’s S-paths theorem. Journal of Combinatorial Theory Ser. B 82, 319–321 (2001)
Sebő, A.: Finding the T-join structure of graphs. Mathematical Programming 36, 123–134 (1986)
Sebő, A.: Factors of Graphs: Structures and Algorithms. Candidate’s thesis, Hungarian Academy of Sciences, Budapest (1987)
Sebő, A.: Undirected distances and the postman structure of graphs. Journal of Combinatorial Theory Ser. B 49, 10–39 (1990)
Sebő, A., Szegő, L.: The path-packing structure of graphs. Egres Technical Report (2003), http://www.cs.elte.hu/egres/tr/egres-03-07.ps
Spille, B., Szegő, L.: A Gallai-Edmonds-type Structure Theorem for Path- Matchings. J. of Graph Theory (2002) (to appear)
Szigeti, Z.: personal communication (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sebő, A., Szegő, L. (2004). The Path-Packing Structure of Graphs. In: Bienstock, D., Nemhauser, G. (eds) Integer Programming and Combinatorial Optimization. IPCO 2004. Lecture Notes in Computer Science, vol 3064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25960-2_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-25960-2_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22113-5
Online ISBN: 978-3-540-25960-2
eBook Packages: Springer Book Archive