Doubly lexical orderings of matrices
SIAM Journal on Computing
All variations on perfectly orderable graphs
Journal of Combinatorial Theory Series B
On the complexity of recognizing perfectly orderable graphs
Discrete Mathematics
Discrete Mathematics
Which claw-free graphs are perfectly orderable?
Discrete Applied Mathematics
Permuting matrices to avoid forbidden submatrices
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
On the complexity of recognizing a class of perfectly orderable graphs
Discrete Applied Mathematics
Recognition of some perfectly orderable graph classes
Discrete Applied Mathematics
Discrete Applied Mathematics
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A graph is an opposition graph, respectively, a coalition graph, if it admits an acyclic orientation which puts the two end-edges of every chordless 4-vertex path in opposition, respectively, in the same direction. Opposition and coalition graphs have been introduced and investigated in connection to perfect graphs. Recognizing and characterizing opposition and coalition graphs still remain long-standing open problems. The present paper gives characterizations for co-bipartite opposition graphs and co-bipartite coalition graphs, and for bipartite opposition graphs. Implicit in our argument is a linear time recognition algorithm for these graphs. As an interesting by-product, we find new submatrix characterizations for the well-studied bipartite permutation graphs.