Treelike Comparability Graphs

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...

Treelike and Chordal Graphs: Algorithms and Generalizations

Beyond the locally treelike approximation for percolation on real networks.

Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally treelike ansatz. Such an approximation, however, holds only to a limited extent, because real graphs are often characterized by high frequencies of short loops. We present here a theoretical framework able to overcome such a limitation for the case of site percolation. Our ...

Multicyclic treelike reflexive graphs

Even and Odd Pairs in Comparability and in P4-comparability Graphs

We characterize even and odd pairs in comparability and in P 4-comparability graphs. The characterizations lead to simple algorithms for deciding whether a given pair of vertices forms an even or odd pair in these classes of graphs. The complexities of the proposed algorithms are O(n + m) for comparability graphs and O(n 2 m) for P 4-comparability graphs. The former represents an improvement ov...