Sentence examples for a split graph from inspiring English sources
A graph is called split graph if its vertex set can be partitioned in a clique K and a stable set S. A split graph is a spider if and only if |K|=|S|≥2 and there exists a bijection f between S and K such that for each v∈S, either N v)={f v)} (thin legs) or N v =K−{f v)} (thick legs).
A split-indifference graph is a split graph that is also an indifference graph.
Every spider is a split graph and therefore it is 2-clique-colourable by Lemma 1.
Then the characteristic graph of G is also a split graph.
We present an algorithm that supports operations for modifying a split graph by adding edges or vertices and deleting edges, such that after each modification the graph is repaired to become a split graph in a minimal way.
Using the split decomposition method [ 42], the data were canonically decomposed into a sum of weakly compatible splits and represented in the form of a splits graph.
First, a collection of weighted splits is constructed from a distance matrix, and then these splits are represented using a splits graph, where a totally compatible collection of splits would be precisely represented as a tree, but incompatible splits as cycles or boxes.
The conflicting information can be retained and interpreted in the form of a "lentoplot" [ 13] or a splits-graph [ 14], with both of these methods implemented in Spectronet [ 15].
The one-complement of this matrix (e.g. a matrix with values scored as 1 - relative frequencies of each clans in PQs) was taken as an estimate of LGTs, and a splits-graph representation [ 50] was used to visualise any conflicts in the phylogenetic forest.
The SPLIT EDITING problem is closely related to SPLIT CLUSTER EDITING as it asks to transform a graph into a (single) split graph by at most k edge modifications.
