منابع مشابه
Redundancy and Helly
The classical Helly’s Theorem about finite sets of convex sets is given an unusually simple proof based on a ‘Redundancy Lemma’. Because the proof is topological it extends immediately to a Helly’s Theorem for the well-known combinatorial topology representation of oriented matroids which is reviewed. The same proof is then used to strengthen Helly’s Theorem in a useful way relative to the Fark...
متن کاملFaster recognition of clique-Helly and hereditary clique-Helly graphs
A family of subsets of a set is Helly when every subfamily of it, which is formed by pairwise intersecting subsets contains a common element. A graph G is cliqueHelly when the family of its (maximal) cliques is Helly, while G is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The best algorithms currently known to recognize clique-Helly and hereditary clique-Helly gra...
متن کاملHelly Numbers of Polyominoes
We define the Helly number of a polyomino P as the smallest number h such that the h-Helly property holds for the family of symmetric and translated copies of P on the integer grid. We prove the following: (i) the only polyominoes with Helly number 2 are the rectangles, (ii) there does not exist any polyomino with Helly number 3, (iii) there exist polyminoes of Helly number k for any k 6= 1, 3.
متن کاملBiclique-Helly Graphs
A graph is biclique-Helly when its family of (maximal) bicliques is a Helly family. We describe characterizations for biclique-Helly graphs, leading to polynomial time recognition algorithms. In addition, we relate biclique-Helly graphs to the classes of clique-Helly, disk-Helly and neighborhood-Helly graphs.
متن کاملHelly Property for Subtrees1
One can prove the following proposition (1) For every non empty finite sequence p holds 〈p(1)〉 aa p = p. Let p, q be finite sequences. The functor maxPrefix(p, q) yields a finite sequence and is defined by: (Def. 1) maxPrefix(p, q) p and maxPrefix(p, q) q and for every finite sequence r such that r p and r q holds r maxPrefix(p, q). Let us observe that the functor maxPrefix(p, q) is commutative...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2001
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0487