@article {IOPORT.05644947, author = {Zenklusen, R. and Ries, B. and Picouleau, C. and de Werra, D. and Costa, M.-C. and Bentz, C.}, title = {Blockers and transversals.}, year = {2009}, journal = {Discrete Mathematics}, volume = {309}, number = {13}, issn = {0012-365X}, pages = {4306-4314}, publisher = {Elsevier Science B.V. (North-Holland), Amsterdam}, doi = {10.1016/j.disc.2009.01.006}, abstract = {Summary: Given an undirected graph $G=(V,E)$ with matching number $\nu (G)$, we define $d$-blockers as subsets of edges $B$ such that $\nu ((V,E\setminus B))\leq \nu (G) - d$. We define $d$-transversals $T$ as subsets of edges such that every maximum matching $M$ has $|M\cap T|\geq d$. We explore connections between $d$-blockers and $d$-transversals. Special classes of graphs are examined which include complete graphs, regular bipartite graphs, chains and cycles and we construct minimum $d$-transversals and $d$-blockers in these special graphs. We also study the complexity status of finding minimum transversals and blockers in arbitrary graphs.}, identifier = {05644947}, }