Permutation bigraphs and interval containments
| Autor: | Pranab K. Saha, Asim Basu, Malay K. Sen, Douglas B. West |
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| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Containment (computer programming) Mathematics::Combinatorics Quantitative Biology::Molecular Networks Applied Mathematics Bigraph Cyclic permutation Combinatorics Permutation Computer Science::Computational Engineering Finance and Science Computer Science::Logic in Computer Science Bipartite graph Computer Science::Programming Languages Discrete Mathematics and Combinatorics Interval (graph theory) Permutation graph Representation (mathematics) Mathematics |
| Zdroj: | Discrete Applied Mathematics. 175:71-78 |
| ISSN: | 0166-218X |
| DOI: | 10.1016/j.dam.2014.05.020 |
| Popis: | A bipartite graph with partite sets X and Y is a permutation bigraph if there are two linear orderings of its vertices such that xy is an edge for x@?X and y@?Y if and only if x appears later than y in the first ordering and earlier than y in the second ordering. We characterize permutation bigraphs in terms of representations using intervals. We determine which permutation bigraphs are interval bigraphs or indifference bigraphs in terms of the defining linear orderings. Finally, we show that interval containment posets are precisely those whose comparability bigraphs are permutation bigraphs, via a theorem showing that a directed version of interval containment provides no more generality than ordinary interval containment representation of posets. |
| Databáze: | OpenAIRE |
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