Split-by-edges trees
Asbj{\o}rn Br{\ae}ndeland

TL;DR
The paper introduces split-by-edges trees, a binary tree structure that encodes the independent sets of a graph, highlighting the relationship between tree leaves and maximum independent sets.
Contribution
It defines the split-by-edges tree structure and explores its properties relating to independent sets and maximum independent sets in graphs.
Findings
Every maximal independent set corresponds to a leaf in the tree.
Maximum independent sets are the closest leaves to the root.
The structure provides insights into the graph's independent sets.
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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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Complexity and Algorithms in Graphs
