To split or to conjoin: the question in image computation

A split system $\mathcal{S}$ on a finite set X, $|X|\ge 3$, is a set of bipartitions or splits of X which contains all splits of the form $\{x,X-\{x\}\}$, $x\in X$. To any such split system $\mathcal{S}$ we can associate the Buneman graph $\mathcal{B}(\mathcal{S})$ which is essentially a median graph with ...$\mathcal{}$$\mathcal{}$${}_{\mathcal{}\mathcal{}}{}_{\mathcal{}\mathcal{}}{}^{}$${}^{}$${}_{\mathcal{}\mathcal{}}$$\mathcal{}\mathcal{}$$\mathcal{}\mathcal{}$$\mathcal{}\mathcal{}$$\mathcal{}$

We study the problem of adding an inclusion minimal set of edges to a given arbitrary graph so that the resulting graph is a split graph, called a minimal split completion of the input graph. Minimal completions of arbitrary graphs into chordal and ...

Split networks are commonly used to visualize collections of bipartitions, also called splits, of a finite set. Such collections arise, for example, in evolutionary studies. Split networks can be viewed as a generalization of phylogenetic trees and may ...