
On nested and 2nested graphs: two subclasses of graphs between threshold and split graphs
A (0,1)matrix has the Consecutive Ones Property (C1P) for the rows if t...
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Structural characterization of some problems on circle and interval graphs
A graph is circle if there is a family of chords in a circle such that t...
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Fast Algorithms for Indices of Nested Split Graphs Approximating Real Complex Networks
We present a method based on simulated annealing to obtain a nested spli...
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Strongly chordal digraphs and Γfree matrices
We define strongly chordal digraphs, which generalize strongly chordal g...
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Minimal obstructions for a matrix partition problem in chordal graphs
If M is an m × m matrix over { 0, 1, ∗}, an Mpartition of a graph G is ...
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Circularly compatible ones, Dcircularity, and proper circulararc bigraphs
In 1969, Alan Tucker characterized proper circulararc graphs as those g...
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On the structure of matrices avoiding intervalminor patterns
We study the structure of 01matrices avoiding a pattern P as an interva...
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2nested matrices: towards understanding the structure of circle graphs
A (0,1)matrix has the consecutiveones 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 2nested matrices, which are (0,1)matrices with a variant of the C1P and for which there is also certain assignment of one of two colors to each block of consecutive 1's in each row. The characterization of 2nested matrices in the present work is of key importance to characterise split graphs that are also circle by minimal forbidden induced subgraphs.
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