A Computational Study for the Graph-theoretic Version of the Union-closed Sets Conjecture
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چکیده
منابع مشابه
A Computational Study for the Graph-Theoretic Version of the Union-Closed Sets Conjecture
An induced subgraph S of a graph G is called a derived subgraph of G if S contains no isolated vertices. An edge e of G is said to be residual if e occurs in more than half of the derived subgraphs of G. We prove some theorems which calculate the number of derived subgraphs for some special graphs. We also present a new algorithm SDSA that calculates the number of derived subgraphs for a given ...
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In 1979 Frankl conjectured that in a finite non-trivial union-closed collection of sets there has to be an element that belongs to at least half the sets. We show that this is equivalent to the conjecture that in a finite non-trivial graph there are two adjacent vertices each belonging to at most half of the maximal stable sets. In this graph formulation other special cases become natural. The ...
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ژورنال
عنوان ژورنال: International Journal of Computer Applications
سال: 2012
ISSN: 0975-8887
DOI: 10.5120/7820-0945