Raphael Machado

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The class C of graphs that do not contain a cycle with a unique chord was recently studied by Trotignon and Vuškovi´c [26], who proved strong structure results for these graphs. In the present paper we investigate how these structure results can be applied to solve the edge-colouring problem in the class. We give computational complexity results for the(More)
BACKGROUND Classical approaches to compute the genomic distance are usually limited to genomes with the same content, without duplicated markers. However, differences in the gene content are frequently observed and can reflect important evolutionary aspects. A few polynomial time algorithms that include genome rearrangements, insertions and deletions (or(More)
BACKGROUND The distance between two genomes is often computed by comparing only the common markers between them. Some approaches are also able to deal with non-common markers, allowing the insertion or the deletion of such markers. In these models, a deletion and a subsequent insertion that occur at the same position of the genome count for two sorting(More)
Classical approaches to compute the genomic distance are usually limited to genomes with the same content and take into consideration only rearrangements that change the organization of the genome (i.e. positions and orientation of pieces of DNA, number and type of chromosomes, etc.), such as inversions, translocations, fusions and fissions. These(More)
A unichord in a graph is an edge that is the unique chord of a cycle. A square is an induced cycle on four vertices. A graph is unichord-free if none of its edges is a unichord. We give a slight restatement of a known structure theorem for unichord-free graphs and use it to show that, with the only exception of the complete graph K 4 , every square-free,(More)
The class of unichord-free graphs was recently investigated in the context of vertex-colouring [J. graphs proved to have a rich structure that can be used to obtain interesting results with respect to the study of the complexity of colouring problems. In particular, several surprising complexity dichotomies of colouring problems are found in subclasses of(More)