A structural characterization for certifying robinsonian matrices

Monique Laurent, M. Seminaroti, Shin-ichi Tanigawa

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original language English P2.21 1-22 22 The Electronic Journal of Combinatorics: EJC 24 2 Published - 5 May 2017

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Interval Graphs
Unit
Weighted Graph
Substructure
Graph in graph theory
Symmetric matrix
Monotone
Efficient Algorithms
Analogue
Imply

Keywords

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

Cite this

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

In: The Electronic Journal of Combinatorics: EJC, Vol. 24, No. 2, P2.21, 05.05.2017, p. 1-22.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Seminaroti, M.

AU - Tanigawa, Shin-ichi

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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.

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KW - seriation

KW - unit interval graph

KW - asteroidal triple

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