### Abstract

Original language | English |
---|---|

Article number | P2.21 |

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | The Electronic Journal of Combinatorics: EJC |

Volume | 24 |

Issue number | 2 |

Publication status | Published - 5 May 2017 |

### Fingerprint

### Keywords

- robinsonian matrix
- seriation
- unit interval graph
- asteroidal triple

### Cite this

*The Electronic Journal of Combinatorics: EJC*,

*24*(2), 1-22. [P2.21].

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*The Electronic Journal of Combinatorics: EJC*, vol. 24, no. 2, P2.21, pp. 1-22.

**A structural characterization for certifying robinsonian matrices.** / Laurent, Monique; Seminaroti, M.; Tanigawa, Shin-ichi.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - A structural characterization for certifying robinsonian matrices

AU - Laurent, Monique

AU - Seminaroti, M.

AU - Tanigawa, Shin-ichi

PY - 2017/5/5

Y1 - 2017/5/5

N2 - A symmetric matrix is Robinsonian if its rows and columns can be simultaneously reordered in such a way that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. The adjacency matrix of a graph is Robinsonian precisely when the graph is a unit interval graph, so that Robinsonian matrices form a matrix analogue of the class of unit interval graphs. Here we provide a structural characterization for Robinsonian matrices in terms of forbidden substructures, extending the notion of asteroidal triples to weighted graphs. This implies the known characterization of unit interval graphs and leads to an efficient algorithm for certifying that a matrix is not Robinsonian.

AB - A symmetric matrix is Robinsonian if its rows and columns can be simultaneously reordered in such a way that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. The adjacency matrix of a graph is Robinsonian precisely when the graph is a unit interval graph, so that Robinsonian matrices form a matrix analogue of the class of unit interval graphs. Here we provide a structural characterization for Robinsonian matrices in terms of forbidden substructures, extending the notion of asteroidal triples to weighted graphs. This implies the known characterization of unit interval graphs and leads to an efficient algorithm for certifying that a matrix is not Robinsonian.

KW - robinsonian matrix

KW - seriation

KW - unit interval graph

KW - asteroidal triple

M3 - Article

VL - 24

SP - 1

EP - 22

JO - The Electronic Journal of Combinatorics: EJC

JF - The Electronic Journal of Combinatorics: EJC

SN - 1097-1440

IS - 2

M1 - P2.21

ER -