Titlebook: Genetic Theory for Cubic Graphs; Pouya Baniasadi,Vladimir Ejov,Michael Haythorpe Book 2016 Springer International Publishing Switzerland 2

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Genetic Theory for Cubic Graphs,t a slightly more complicated descendant. We prove that every descendant can be constructed from a family of genes via the use of our six operations, and state the result (to be proved in Chap. 3) that this family is unique for any given descendant.

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Inherited Properties of Descendants,ively, 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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Uniqueness of Ancestor Genes, graph has cardinality which is a fixed constant for that graph. We then proceed to prove that for any descendant without parthenogenic objects, it is possible to isolate at least two genes with single inverse breeding operations. Finally, we use each of these results to prove the uniqueness theorem.

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Book 2016lesman Problem) may be “inherited” from simpler graphs which – in an appropriate sense – could be seen as “ancestors” of the given graph instance. The authors propose a partitioning of the set of unlabeled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardi

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