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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Thomas Lange
University of Applied Sciences Mittweida Technikumplatz 17, 09648 Mittweida, Germany
Electrical & Electronics Engineering

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Representing non-crossing cuts by phylogenetic trees Thomas Lange
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.20

Abstract

Phylogenetic trees are representations of the evolutionary descendency of a set of species. In graph-theoretic terms, a phylogenetic tree is a partially labeled tree where unlabeled vertices have at least degree three and labels corresponds to pairwise disjoint subsets of the set of species. A cut of a graph G = (V, E) is defined as bipartition {S, V \ S} of the vertex set V of G. A pair of cuts {S, S}, {T, T} is said to be crossing, if neither S ∩ T, S ∩ T, S ∩ T nor S ∩ T is empty. In this paper, we show that each set of pairwise non-crossing cuts of a graph G can be represented uniquely by a phylogenetic tree such that the set of species corresponds to the vertex set of G.
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