Multicyclic treelike reflexive graphs

Multicyclic treelike reflexive graphs

Treelike Comparability Graphs

A comparability graph is a simple graph which admits a transitive orientation on its edges. Each one of such orientations defines a poset on the vertex set, and also it is said that this graph is the comparability graph of the poset. A treelike poset is a poset whose covering graph is a tree. Comparability graphs of arborescence posets are known as trivially perfect graphs. These have been char...

Modularity of regular and treelike graphs

Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the modularity of two kinds of graphs. For r-regular graphs with a given number of vertices, we investigate the minimum possible modularity, the typical modulari...

Treelike and Chordal Graphs: Algorithms and Generalizations

Treelike Comparability Graphs: Characterization, Recognition, and Applications

An undirected graph is a treelike comparability graph if it admits a transitive orientation such that its transitive reduction is a tree. We show that treelike comparability graphs are distance hereditary. Utilizing this property, we give a linear time recognition algorithm. We then characterize permutation graphs that are treelike. Finally, we consider the Partitioning into Bounded Cliques pro...