Skip to main content
SpringerLink
Log in

Induced Graph Packing Problems

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

Let \({\mathcal{H}}\) be a set of undirected graphs. The induced \({\mathcal{H}}\) -packing problem in an input graph G is to find a subgraph Q of G of maximum size such that each connected component of Q is an induced subgraph of G and is isomorphic to some member of \({\mathcal{H}}\) . In this paper we focus on the case when \({\mathcal{H}}\) consists of factor-critical graphs and a certain family of ‘propellers’. Clarifying the methods developed in the related theory of non-induced graph packings, we show a Gallai–Edmonds type structure theorem and a Berge–Tutte type minimax formula. We also give an Edmonds type alternating forest algorithm for the case when \({\mathcal{H}}\) consists of a sequential set of stars and factor-critical graphs. This simplifies the related result of Egawa, Kano and Kelmans.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cornuéjols G., Hartvigsen D.: An extension of matching theory. J. Combin. Theory Ser. B 40, 285–296 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cornuéjols G., Hartvigsen D., Pulleyblank W.: Packing subgraphs in a graph. Oper. Res. Lett. 1, 139–143 (1981/82)

    Article  MathSciNet  Google Scholar 

  3. Cornuéjols G., Pulleyblank W.: Perfect triangle-free 2-matchings. Math. Prog. Study 13, 1–7 (1980)

    MATH  Google Scholar 

  4. Edmonds J.: Paths, trees, and flowers. Can. J. Math. 17, 449–467 (1965)

    MATH  MathSciNet  Google Scholar 

  5. Edmonds J., Fulkerson D.R.: Transversals and matroid partition. J. Res. Nat. Bur. Stand. Sect. B 69, 147–153 (1965)

    MATH  MathSciNet  Google Scholar 

  6. Egawa Y., Kano M., Kelmans A.K.: Star partitions of graphs. J. Graph Theory 25, 185–190 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gallai T.: Kritische Graphen II. A Magy. Tud. Akad. Mat. Kut. Int. Közl. 8, 135–139 (1963)

    MATH  MathSciNet  Google Scholar 

  8. Gallai T.: Maximale Systeme unabhängiger Kanten. A Magy. Tud. Akad. Mat. Kut. Int. Közl. 9, 401–413 (1964)

    MATH  MathSciNet  Google Scholar 

  9. Hoffman A.J., Kuhn H.W.: Systems of distinct representatives and linear programming. Am. Math. Mon. 63, 455–460 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kelmans A.K.: Optimal packing of induced stars in a graph. Discrete Math. 173, 97–127 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Király, Z., Szabó, J.: Generalized induced factor problems. Technical Report TR-2002-07. Egerváry Research Group, Budapest. http://www.cs.elte.hu/egres (2002)

  12. Kirkpatrick D.G., Hell P.: On the complexity of general graph factor problems. SIAM J. Comput. 12, 601–609 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  13. Las Vergnas M.: An extension of Tutte’s 1-factor theorem. Discrete Math. 23, 241–255 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  14. Loebl M., Poljak S.: Efficient subgraph packing. KAM-DIMATIA Series 1987-50

  15. Loebl M., Poljak S.: On matroids induced by packing subgraphs. J. Combin. Theory Ser. B 44, 338–354 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  16. Loebl M., Poljak S.: Efficient subgraph packing. J. Combin. Theory Ser. B 59, 106–121 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Lovász L.: Subgraphs with prescribed valencies. J. Combin. Theory 8, 391–416 (1970)

    Article  MATH  Google Scholar 

  18. Mendelsohn N.S., Dulmage A.L.: Some generalizations of the problem of distinct representatives. Can. J. Math. 10, 230–241 (1958)

    MATH  MathSciNet  Google Scholar 

  19. Saito A., Watanabe M.: Partitioning graphs into induced stars. Ars Combin. 36, 3–6 (1993)

    MATH  MathSciNet  Google Scholar 

  20. Schrijver A.: Combinatorial Optimization. Polyhedra and Efficiency Algorithms and Combinatorics, vol. 24. Springer, Berlin (2003)

    Google Scholar 

  21. Szabó, J.: Graph packings and the degree prescribed factor problem. PhD thesis, Eötvös University, Budapest. http://www.cs.elte.hu/~jacint (2006)

  22. Tutte W.T.: The factors of graphs. Can. J. Math. 4, 314–328 (1952)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and CNL, Eötvös University, Pázmány P. s. 1/C, Budapest, 1117, Hungary

    Zoltán Király

  2. MTA-ELTE Egerváry Research Group (EGRES), Department of Operations Research, Eötvös University, Pázmány P. s. 1/C, Budapest, 1117, Hungary

    Jácint Szabó

Authors
  1. Zoltán Király
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jácint Szabó
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zoltán Király.

Additional information

Z. Király research was supported by EGRES group (MTA-ELTE) and OTKA grants CNK 77780, K 60802 and NK 67867. J. Szabó research was supported by OTKA grants K60802, TS049788 and by European MCRTN Adonet, Contract Grant No. 504438.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Király, Z., Szabó, J. Induced Graph Packing Problems. Graphs and Combinatorics 26, 243–257 (2010). https://doi.org/10.1007/s00373-010-0906-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-010-0906-0

Keywords

Search

Navigation