منابع مشابه
Common Transversals
Given t families, each family consisting of s finite sets, we show that if the families “separate points" in a natural way, and if the union of all the sets in all the families contains more than (s+1)t st 1 1 elements, then a common transversal of the t families exists. In case each family is a covering family, the bound is st st 1. Both of these bounds are best possible. This work extends rec...
متن کاملConvex Transversals
We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?” We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem re...
متن کاملBlockers 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...
متن کاملTransversals of Longest Paths
Let lpt(G) be the minimum cardinality of a set of vertices that intersects all longest paths in a graph G. Let ω(G) be the size of a maximum clique in G, and tw(G) be the treewidth of G. We prove that lpt(G) ≤ max{1,ω(G)− 2} when G is a connected chordal graph; that lpt(G) = 1 when G is a connected bipartite permutation graph or a connected full substar graph; and that lpt(G) ≤ tw(G) for any co...
متن کاملPermanent rank and transversals
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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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1982
ISSN: 0095-8956
DOI: 10.1016/0095-8956(82)90035-1