Complexity of representation of graphs by set systems
نویسندگان
چکیده
Let .F be a family of subsets of S and let G be a graph with vertex set V= {XA IA E .Y) such that: (.K~,xB) is an edge iffAnB#O. The family .F is called a set representation of the graph G. It is proved that the problem of finding minimum k such that G can be represented by a family of sets of cardinality at most k is NP-complete. Moreover, it is NP-complete to decide whether a graph can be represented by a family of distinct 3-element sets. The set representations of random graphs are also considered.
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ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 3 شماره
صفحات -
تاریخ انتشار 1981