All formalizations of MDS structure of micronuclear or intermediate genes that we have considered until now (viz., micronuclear arrangements, MDS descriptors, and legal strings) were done in the framework of strings. We will move now to a different mathematical framework by formalizing MDS structure of genes as graphs. This transition from strings to graphs is obtained by considering the overlap graphs of legal strings. Each pointer set occurring in a legal string determines the substring of this string delimited by the two occurrences of this pointer set, and the overlap graph of a legal string represents the overlapping structures of all such substrings. In this chapter we introduce the basic notions concerning overlap graphs and study their relationship to (realistic) legal strings.
KeywordsSimple Graph Hamiltonian Path Signed Graph Circle Graph Chord Diagram
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