Inherited Properties of Descendants

Part of the SpringerBriefs in Operations Research book series (BRIEFSOPERAT)


Given the results of Chap. 1 that every descendant may be constructed from a complete family of ancestor genes, we now investigate how the properties of the descendant correspond to the properties of those genes. In particular we consider the properties of Hamiltonicity, bipartiteness and planarity. In all three cases we prove that a descendant may only possess the property if all of its ancestor genes do. In the case of bipartiteness and planarity we also establish sufficient conditions. These results allow us to analyse the properties of a graph by considering its ancestor genes, or alternatively, to construct a graph with desired properties by choosing smaller genes with those properties. We follow each section with a discussion of famous results and conjectures relating to the graph properties, and how the results of this chapter relate to them.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of CSEMFlinders UniversityBedford ParkAustralia

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