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In graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set.
The graph is based on datasets by Jörger et al. (2010) [1] and generated by SplitsTree. A split in phylogenetics is a bipartition of a set of taxa, and the smallest unit of information in unrooted phylogenetic trees: each edge of an unrooted phylogenetic tree represents one split, and the tree can be efficiently reconstructed from its set of ...
In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. The splits of a graph can be collected into a tree-like structure called the split decomposition or join decomposition , which can be constructed in linear time.
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem. 2.
An unrooted phylogenetic network N on X is any undirected graph whose leaves are bijectively labeled by the taxa in X. A number of different types of unrooted phylogenetic networks are in use like split networks and quasi-median networks. In most cases, such networks only depict relations between taxa, without giving information about the ...
In biology, pairwise interactions have historically been the focus of intense study. With the recent advances in network science , it has become possible to scale up pairwise interactions to include individuals of many species involved in many sets of interactions to understand the structure and function of larger ecological networks . [ 29 ]
The search for a new Chicago Bears coach is on in earnest with the conclusion of the NFL's regular season, and it reportedly includes a surprising new candidate.
A perfect graph is a graph in which the clique number equals the chromatic number in every induced subgraph. A split graph is a graph in which some clique contains at least one endpoint of every edge. A triangle-free graph is a graph that has no cliques other than its vertices and edges.