2-nested matrices: towards understanding the structure of circle graphs
Guillermo Durán,
Nina Pardal,
Martín D. Safe
Abstract:A (0, 1)-matrix has the consecutive-ones property (C1P) if its columns can be permuted to make the 1's in each row appear consecutively. This property was characterised in terms of forbidden submatrices by Tucker in 1972. Several graph classes were characterised by means of this property, including interval graphs and strongly chordal digraphs.In this work, we define and characterise 2-nested matrices, which are (0, 1)matrices with a variant of the C1P and for which there is also certain assignment of one of t… Show more
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