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For a graph property X, let X n be the number of graphs with vertex set {1,. .. , n} having property X, also known as the speed of X. A property X is called factorial if X is hereditary (i.e. closed under taking induced subgraphs) and n c 1 n ≤ X n ≤ n c 2 n for some positive constants c 1 and c 2. Hereditary properties with the speed slower than factorial(More)
An induced matching M in a graph G is dominating if every edge not in M shares exactly one vertex with an edge in M. The dominating induced matching problem (also known as efficient edge domination) asks whether a graph G contains a dominating induced matching. This problem is generally NP-complete, but polynomial-time solvable for graphs with some special(More)
An extremal point of a positive threshold Boolean function f is either a maximal zero or a minimal one. It is known that if f depends on all its variables, then the set of its extremal points completely specifies f within the universe of threshold functions. However, in some cases, f can be specified by a smaller set. The minimum number of points in such a(More)
Independent domination is one of the rare problems for which the complexity of weighted and unweighted versions is known to be different in some classes of graphs. In the present paper, we prove two NP-hardness results, one for the weighted version and one for unweighted, which tighten the gap between them. We also prove that both versions of the problem(More)
In morpha l l ax i s , r egene ra t ion takes p lace by redeve lopment of the remnant of the organ into a c o m plete s t ruc tu re of cor responding ly s m a l l e r s ize. In this p r o c e s s cel l p ro l i f e ra t ion p lays a min imal role , and the p r o c e s s is accompl ished mainly by d i sp lacement of cel l ma te r i a l . This method is found(More)