Robust recoverable perfect matchings

We study perfect matchings M in graphs G that have the two properties of being robust as well as recoverable; where robust means that the failure of a set F' of not too many edges of G can be compensated, and recoverable means that this compensation can be done in an efficient way, that is, G-F' has a perfect matching M' for which the symmetric difference of M and M' is small. We establish the hardness of several related algorithmic problems and identify some tractable cases. Among others we show the hardness of the well known matching preclusion number of a graph. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 663, 210-213 2015

[1]  Eddie Cheng,et al.  Matching preclusion and Conditional Matching preclusion for Augmented Cubes , 2010, J. Interconnect. Networks.

[2]  Insung Ihm,et al.  Strong matching preclusion , 2011, Theor. Comput. Sci..

[3]  Eddie Cheng,et al.  Matching Preclusion and Conditional Matching Preclusion Problems for Twisted Cubes , 2010 .

[4]  Xianyue Li,et al.  Matching preclusion for balanced hypercubes , 2012, Theor. Comput. Sci..

[5]  Eddie Cheng,et al.  Matching preclusion and conditional matching preclusion for bipartite interconnection networks II: Cayley graphs generated by transposition trees and hyper‐stars , 2012, Networks.

[6]  Ali Ridha Mahjoub,et al.  On the NP-completeness of the perfect matching free subgraph problem , 2012, Theor. Comput. Sci..

[7]  Dominique de Werra,et al.  Blockers and transversals , 2009, Discret. Math..

[8]  Eddie Cheng,et al.  Matching preclusion and Conditional Matching preclusion for Crossed Cubes , 2012, Parallel Process. Lett..

[9]  Fábio Protti,et al.  Matching Preclusion Number in Cartesian Product of Graphs and its Application to Interconnection Networks , 2013, Ars Comb..

[10]  E. Cheng,et al.  Matching preclusion for some interconnection networks , 2007 .

[11]  Insung Ihm,et al.  Strong matching preclusion under the conditional fault model , 2013, Discret. Appl. Math..

[12]  Eddie Cheng,et al.  Matching preclusion and conditional matching preclusion for regular interconnection networks , 2012, Discret. Appl. Math..

[13]  Eddie Cheng,et al.  Matching preclusion and conditional matching preclusion for bipartite interconnection networks I: Sufficient conditions , 2012, Networks.

[14]  Rico Zenklusen,et al.  Matching interdiction , 2008, Discret. Appl. Math..

[15]  Eddie Cheng,et al.  Matching preclusion for Alternating Group Graphs and their Generalizations , 2008, Int. J. Found. Comput. Sci..

[16]  Kai Feng,et al.  Strong matching preclusion for k-ary n-cubes , 2013, Discret. Appl. Math..

[17]  D. de Werra,et al.  Blockers and transversals in some subclasses of bipartite graphs: When caterpillars are dancing on a grid , 2010, Discret. Math..