Strongly chordal digraphs and Γ-free matrices

by   Pavol Hell, et al.

We define strongly chordal digraphs, which generalize strongly chordal graphs and chordal bipartite graphs, and are included in the class of chordal digraphs. They correspond to square 0,1 matrices that admit a simultaneous row and column permutation avoiding the Γ matrix. In general, it is not clear if these digraphs can be recognized in polynomial time, and we focus on symmetric digraphs (i.e., graphs with possible loops), tournaments with possible loops, and balanced digraphs. In each of these cases we give a polynomial-time recognition algorithm and a forbidden induced subgraph characterization.


page 1

page 2

page 3

page 4


Biclique Graphs of K_3-free Graphs and Bipartite Graphs

A biclique of a graph is a maximal complete bipartite subgraph. The bicl...

An Algorithm for Generating Strongly Chordal Graphs

Strongly chordal graphs are a subclass of chordal graphs. The interest i...

Integer programs with bounded subdeterminants and two nonzeros per row

We give a strongly polynomial-time algorithm for integer linear programs...

On classes of graphs with strongly sublinear separators

For real numbers c,epsilon>0, let G_c,epsilon denote the class of graphs...

Weak consistency of P-time event graphs

P-time event graphs (P-TEGs) are event graphs where the residence time o...

Strongly Connected Components in Stream Graphs: Computation and Experimentations

Stream graphs model highly dynamic networks in which nodes and/or links ...

2-nested matrices: towards understanding the structure of circle graphs

A (0,1)-matrix has the consecutive-ones property (C1P) if its columns ca...