منابع مشابه
Independent Transversals and Independent Coverings in Sparse Partite Graphs
An [n, k, r]-partite graph is a graph whose vertex set, V , can be partitioned into n pairwisedisjoint independent sets, V1, . . . , Vn, each containing exactly k vertices, and the subgraph induced by Vi ∪ Vj contains exactly r independent edges, for 1 ≤ i < j ≤ n. An independent transversal in an [n, k, r]-partite graph is an independent set, T , consisting of n vertices, one from each Vi. An ...
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A covering of a multigraph G is a subset of edges which meet ail vertices of G. Partitions of the edges of G into coverings Ci, C2,..., Ck are considered. In particular we examine how close the cardinalities of thèse coverings may be. A resuit concerning matchings is extended to the décomposition into coverings. Finally thèse considérations are generalized to the décompositions of the vertices ...
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We consider the problem of enumerating all minimal hitting sets of a given hypergraph (V,R), where V is a finite set, called the vertex set andR is a set of subsets of V called the hyperedges. We show that, when the hypergraph admits a balanced subdivision, then a recursive decomposition can be used to obtain efficiently all minimal hitting sets of the hypergraph. We apply this decomposition fr...
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V. Chv atal proved that no minimal imperfect graph has a small transversal, that is, a set of vertices of cardinality at most + ! 1 which meets every !-clique and every -stable set. In this paper we prove that a slight generalization of this notion of small transversal leads to a conjecture which is as strong as Berge's Strong Perfect Graph Conjecture for a very large class of graphs, although ...
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Given a closed, irreducible 3–manifold, its complexity is the minimum number of tetrahedra in a (pseudosimplicial) triangulation of the manifold. This number agrees with the complexity defined by Matveev [5] unless the manifold is S , RP or L.3; 1/. The complexity for an infinite family of closed manifolds has first been given by the authors in [4]. The family consisted of lens spaces having a ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1978
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90008-0