He Zhen: Minimum tP_3-saturation Graphs

Abstract: A graph G is H-saturated if G does not contain H as a
subgraph, but the addition of any edge between two nonadjacent vertices
in G results in a copy of H in G. The saturation number sat(n,H) is the
minimum number of edges in a n-vertex H-saturated. For a graph F, let
tF denote the disjoint union of t copies of F. Faudree, Faudree and
Schmitt proposed a problem that is to determine sat(n,tP_k) for all t
and k.  For t ≥ 1 and n ≥ 10t, we give a lower bound on sat(n,tP_3).

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