Split-by-edges trees

A split-by-edges tree of a graph G on n vertices is a binary tree T where the root = V(G), every leaf is an independent set in G, and for every other node N in T with children L and R there is a pair of vertices {u, v} in N such that L = N - v, R = N - u, and uv is an edge in G. It follows from the definition that every maximal independent set in G is a leaf in T, and the maximum independent sets of G are the leaves closest to the root of T.Comment: The definition of 'ordered SBE-tree' has been added. This corrects an omission in the previous versions but does not change anything essential. Some changes have been made to accommodate the addition, and others have been made to correct minor errors and improve wording

Depth-first search in split-by-edges trees

A layerwise search in a split-by-edges tree (as defined by Br{\ae}ndeland, 2015) of agiven graph produces a maximum independent set in exponential time. A depth-first search produces an independent set, which may or may not be a maximum, in linear time, but the worst case success rate is maybe not high enough to make it really interesting. What may make depth-first searching in split-by-edges trees interesting, though, is the pronounced oscillation of its success rate along the graph size axis.Comment: 3 page

A family of greedy algorithms for finding maximum independent sets

The greedy algorithm A iterates over a set of uniformly sized independent sets of a given graph G and checks for each set S which non-neighbor of S, if any, is best suited to be added to S, until no more suitable non-neighbors are found for any of the sets. The algorithms receives as arguments the graph, the heuristic used to evaluate the independent set candidates, and the initial cardinality of the independent sets, and returns the final set of independent sets.Comment: 4 page