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Uniquely C4-Saturated Graphs ∗

By Joshua Cooper, Timothy D. Lesaulnier, Paul S. Wenger and Douglas B. West


For a fixed graph H, a graph G is uniquely H-saturated if G does contain H, but the addition of any edge from G to G completes exactly one copy of H. Using a combination of algebraic methods and counting arguments, we determine all the uniquely C4-saturated graphs; there are only ten of them.

Year: 2010
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