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The maximum internal spanning tree (MIST) problem is utilized to determine a spanning tree in a graph G, with the maximum number of possible internal vertices. The incremental maximum internal spanning tree (IMIST) problem is the incremental version of MIST whose feasible solutions are edge-sequences e 1 , e 2 , . . . , e n−1 such that the first k edges form trees for all k ∈|In(T k )| with lower being better. Here, opt(G, k) denotes the number of internal vertices in a tree with k edges in G, which has the largest possible number of internal vertices, and |In(T k )| is the number of internal vertices in the tree comprising the solution's first k edges. We first obtained an IMIST algorithm with a competitive ratio of 2, followed by a 12/7-competitive algorithm based on an approximation algorithm for MIST.

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