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A characterization of PM-compact Hamiltonian bipartite graphs

A characterization of PM-compact Hamiltonian bipartite graphs 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A characterization of PM-compact Hamiltonian bipartite graphs

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Publisher
Springer Journals
Copyright
Copyright © 2015 by The Editorial Office of AMAS & Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-015-0475-3
Publisher site
See Article on Publisher Site

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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jun 19, 2015

References