منابع مشابه
Blockers and transversals
Given G = (V,E) an undirected graph with matching number ν(G), we define d-blockers as subsets of edges B such that ν(G′ = (V,E \B)) ≤ ν(G)−d. We define d-transversals T as subsets of edges such that every maximum matchingM has |M ∩T | ≥ d. We explore connections between d-blockers and d-transversals. Special classes of graphs are examined which include complete graphs, regular bipartite graphs...
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We consider a set V of elements and an optimization problem on V : the search for a maximum (or minimum) cardinality subset of V verifying a given property P. A d-transversal is a subset of V which intersects any optimum solution in at least d elements while a d-blocker is a subset of V whose removal deteriorates the value of an optimum solution by at least d. We present some general characteri...
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We use the polynomial method of Alon to give a sufficient condition for the existence of partial transversals in terms of the permanent rank of a certain matrix.
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In sec tion 1, transversal Inatroids are assoc iated with "syste ms of di s tinct represe ntatives" (i. e., tra nsversals) and,. more generally , matc hing matroids are associated with matc hings in graphs . Th e transversal matrolds and a theore m of P. J. Higgins on disjoint transversals of a famil y of se ts , along wIth th e well-known graphIc matrold s a nd some theorems on decomposition o...
متن کاملTransversals and Multitransversals
A transversal of a family .Fof sets is a family of pairwise distinct elements, one from each member of .y , and a multitransversal of .IF is a family of pairwise disjoint subsets, one of each member of F . The main result of this note, Theorem 4, gives necessary and sufficient conditions on families sa/ and .4 of cardinals in order that every family J whose members have cardinals given by sl sh...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.01.006