Generalized subgraph-restricted matchings in graphs

For a graph property P, we define a P-matching as a set M of disjoint edges such that the subgraph induced by the vertices incident to M has property P. Previous examples include strong/induced matchings and uniquely restricted matchings. We explore the general properties of P-matchings, but especially the cases where P is the property of being acyclic or the property of being disconnected. We consider bounds on and the complexity of the maximum cardinality of a P-matching and the minimum cardinality of a maximal P-matching.

[1]  A. Brandstädt,et al.  Graph Classes: A Survey , 1987 .

[2]  Robert C. Vandell,et al.  Decycling graphs , 1997, Journal of Graph Theory.

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Robert C. Vandell,et al.  Decycling graphs , 1997 .

[5]  Wayne Goddard,et al.  Hereditary domination and independence parameters , 2004, Discuss. Math. Graph Theory.

[6]  F. B. Shepherd,et al.  Adding an identity to a totally unimodular matrix , 1994 .

[7]  Vijay V. Vazirani,et al.  NP-Completeness of Some Generalizations of the Maximum Matching Problem , 1982, Inf. Process. Lett..

[8]  Martin Charles Golumbic,et al.  Irredundancy in Circular Arc Graphs , 1993, Discret. Appl. Math..

[9]  Danuta Michalak.  Domination, independence and irredundance with respect to additive induced-hereditary properties , 2004, Discret. Math..

[10]  Angelika Steger,et al.  On induced matchings , 1993, Discret. Math..

[11]  A. El Maftouhi.  The minimum size of a maximal strong matching in a random graph , 1995, Australas. J Comb..

[12]  Ronald V. Book,et al.  Review: Michael R. Garey and David S. Johnson, Computers and intractability: A guide to the theory of $NP$-completeness , 1980 .

[13]  Moshe Lewenstein,et al.  Uniquely Restricted Matchings , 2001, Algorithmica.

[14]  Michele Zito.  Linear Time Maximum Induced Matching Algorithm for Trees , 2000, Nord. J. Comput..

[15]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[16]  Michele Zito.  Induced Matchings in Regular Graphs and Trees , 1999, WG.

[17]  Daniel Hershkowitz,et al.  Ranks of zero patterns and sign patterns , 1993 .

[18]  Moshe Lewenstein,et al.  New results on induced matchings , 2000, Discret. Appl. Math..

[19]  L. Sunil Chandran,et al.  A Linear Time Algorithm for Enumerating All the Minimum and Minimal Separators of a Chordal Graph , 2001, COCOON.

[20]  M. Plummer.  Matching and Vertex Packing: How “hard” are They? , 1993 .

[21]  Zsolt Tuza,et al.  Induced matchings in bipartite graphs , 1989, Discret. Math..