Skip to main content
SpringerLink
Log in

A characterization of PM-compact Hamiltonian bipartite graphs

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. A graph is called perfect matching compact (shortly, PM-compact), if its perfect matching polytope has diameter one. This paper gives a complete characterization of simple PM-compact Hamiltonian bipartite graphs. We first define two families of graphs, called the H2C-bipartite graphs and the H23-bipartite graphs, respectively. Then we show that, for a simple Hamiltonian bipartite graph G with |V(G)| ≥ 6, G is PM-compact if and only if G is K 3,3, or G is a spanning Hamiltonian subgraph of either an H2C-bipartite graph or an H23-bipartite graph.

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. Bian, H.P., Zhang, F.J. The graph of perfect matching polytope and an extreme problem. Discrete Mathematics. 309: 5017–5023 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bondy, J.A., Murty, U.S.R. Graph Theory. Springer-Verlag, Berlin, 2008

    Book  MATH  Google Scholar 

  3. Chvátal, V. On certain polytopes associated with graphs. Journal of Combinatorial Theory (B). 18: 138–154 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lovász, L., Plummer, M.D. Matching Theory. Elsevier Science Publishers, B.V. North Holland, 1986

    MATH  Google Scholar 

  5. Naddef, D.J., Pulleyblank, W.R. Hamiltonicity in (0-1)-polytope. Journal of Combinatorial Theory (B), 37: 41–52 (1984)

    Article  MATH  Google Scholar 

  6. Padberg, M.W., Rao, M.R. The travelling salesman problem and a class of polyhedra of diameter two. Mathematical Programming. 7: 32–45 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. Schrijver, A. Combinatorial Optimization: Polyhedra and Efficiency. Springer-Verlag, Berlin, 2003

    MATH  Google Scholar 

  8. Wang, X.M., Shang, W.P., Lin, Y.X. A characterization of claw-free PM-compact cubic Graphs. Discrete Mathematics, Algorithms and Applications, 6(2): 1450025 (5 pages) (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, China

    Xiu-mei Wang, Jin-jiang Yuan & Yi-xun Lin

Authors
  1. Xiu-mei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jin-jiang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yi-xun Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiu-mei Wang.

Additional information

Supported by the National Natural Science Foundation of China under Grant No. 11101383, 11271338 and 11201432.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Xm., Yuan, Jj. & Lin, Yx. A characterization of PM-compact Hamiltonian bipartite graphs. Acta Math. Appl. Sin. Engl. Ser. 31, 313–324 (2015). https://doi.org/10.1007/s10255-015-0475-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-015-0475-3

Keywords

2000 MR Subject Classification

Search

Navigation