Evaluating the Tutte polynomial at (1,1) ["one comma one"] gives the number of these things.
Evaluating the Tutte polynomial at (1,1) ["one comma one"] gives the number of these things. Kirchoff's theorem uses the Laplacian matrix's eigenvalues to find the number of them. Boruvka's algorithm for finding a specific type of these things runs in big-O of E log V time. The reverse-delete algorithm finds a type of these things by deleting the edge with the largest weight whose removal would not disconnect the graph. For a complete graph, there are n to the power of n minus two of them, according to Cayley's formula.They cannot exist in unconnected graphs, and they are acyclic subgraphs containing every vertex. For 10 points -- Prim's and Kruskal's algorithms find "minimal" cost examples of what subgraphs?
Evaluating the Tutte polynomial at (1,1) ["one comma one"] gives the number of these things.
minimum spanning trees [prompt on partial answer, accept spanning forests before "unconnected"]