Helly property, clique raphs, complementary graph classes, and sandwich problems
نویسندگان
چکیده
منابع مشابه
Faster 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 کاملGraph sandwich problems
A sandwich problem for a graph with respect to a graph property Π is a partially specified graph, i.e., only some of the edges and non-edges are given, and the question to be answered is, can this graph be completed to a graph which has the property Π? The graph sandwich problem was investigated for a large number of families of graphs in a 1995 paper by Golumbic, Kaplan and Shamir, and much su...
متن کاملOn hereditary clique-Helly self-clique graphs
A graph is clique-Helly if any family of mutually intersecting (maximal) cliques has non-empty intersection, and it is hereditary clique-Helly (abbreviated HCH) if its induced subgraphs are clique-Helly. The clique graph of a graph G is the intersection graph of its cliques, and G is self-clique if it is connected and isomorphic to its clique graph. We show that every HCH graph is an induced su...
متن کاملComputational Complexity of Classical Problems for Hereditary Clique-helly Graphs
A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of th...
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: Journal of the Brazilian Computer Society
سال: 2008
ISSN: 0104-6500,1678-4804
DOI: 10.1007/bf03192558