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SIAM Journal on Computing
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Discrete Applied Mathematics
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SIAM Journal on Computing
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Recognizing interval digraphs and interval bigraphs in polynomial time
Discrete Applied Mathematics
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European Journal of Combinatorics
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Information Processing Letters
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Discrete Applied Mathematics
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Discrete Applied Mathematics
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Journal of Graph Theory
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Discrete Applied Mathematics
Bandwidth of convex bipartite graphs and related graphs
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Bandwidth of convex bipartite graphs and related graphs
Information Processing Letters
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An orthogonal ray graph is an intersection graph of horizontal and vertical rays (half-lines) in the xy-plane. An orthogonal ray graph is a 2-directional orthogonal ray graph if all the horizontal rays extend in the positive x-direction and all the vertical rays extend in the positive y-direction. We first show that the class of orthogonal ray graphs is a proper subset of the class of unit grid intersection graphs. We next provide several characterizations of 2-directional orthogonal ray graphs. Our first characterization is based on forbidden submatrices. A characterization in terms of a vertex ordering follows immediately. Next, we show that 2-directional orthogonal ray graphs are exactly those bipartite graphs whose complements are circular arc graphs. This characterization implies polynomial-time recognition and isomorphism algorithms for 2-directional orthogonal ray graphs. It also leads to a characterization of 2-directional orthogonal ray graphs by a list of forbidden induced subgraphs. We also show a characterization of 2-directional orthogonal ray trees, which implies a linear-time algorithm to recognize such trees. Our results settle an open question of deciding whether a (0,1)-matrix can be permuted to avoid the submatrices [1001]and[1011].