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Extremal problems involving neighborhood unions. (English) Zbl 0659.05058
The authors continue their study of extremal problems for graphs that satisfy the property that $$| N(x)\cup N(y)| \geq s$$ for every pair of nonadjacent vertices $$x,y\in V(G)$$. [See R. Faudree et al., “Neighborhood unions and Hamiltonian properties in graphs”, J. Comb. Theory., Ser. B (to appear).] In this paper, values of s are found that ensure that the graph contains an s-matching, a 1-factor, a path of a specific length, or a cycle of a particular length.
Reviewer: R.L.Hemminger

MSC:
 05C35 Extremal problems in graph theory 05C45 Eulerian and Hamiltonian graphs 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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