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arXiv · 1504.07626

Split-by-edges trees

Asbjørn Brændeland
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Abstract

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.

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Asbjørn Brændeland. 2015-04-28. Split-by-edges trees. https://arxiv.org/abs/1504.07626

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