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Define a simple graph G to be k-superuniversal iff for any k-element simple graph K and for any full subgraph H of K every full embedding of H into G can be extended to a full embedding of K into G. We prove that for each positive integer k there exist finite k-superuniversal graphs, and e find upper and looer bounds on the smallest such graphs. We also(More)
In his paper on subsets of the series of natural numbers N. Lusin [2] defines two sets F, G g co to be orthogonal (F I G) iff F c3 G is finite. A family (henceforth the term family will be used only to denote subsets of the power set of co) is said to be internally orthogonal iff for any two distinct members F, G of ~ we have F 2. G. Two families ~ and ~(More)
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