1.Mathematics Department,University of South Carolina,Columbia,USA;2.Mathematics Department,University of Illinois,Urbana,USA;3.Department of Mathematical and Statistical Sciences,University of Colorado Denver,Denver,USA
Abstract:
For a fixed graph H, a graph G is uniquely H-saturated if G does not contain H, but the addition of any edge from [`(G)]{overline{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.
