Split-by-edges trees
Data Structures and Algorithms
2015-05-14 v3 Discrete Mathematics
Combinatorics
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.
Keywords
Cite
@article{arxiv.1504.07626,
title = {Split-by-edges trees},
author = {Asbjørn Brændeland},
journal= {arXiv preprint arXiv:1504.07626},
year = {2015}
}
Comments
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 wordings