rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Genetic Theory for Cubic Graphs
  name:
    name part: Baniasadi, Pouya.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Ejov, Vladimir.
    role:
      role term: author.
  name:
    name part: Filar, Jerzy A.
    role:
      role term: author.
  name:
    name part: Haythorpe, Michael.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 118 p. 85 illus., 8 illus. in color. online resource.
  abstract: This book was motivated by the notion that some of the underlying difficulty in challenging instances of graph-based problems (e.g., the Traveling Salesman 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 cardinality of the descendants dominates that of the genes. The key distinction between the two subsets is the presence of special edge cut sets, called cubic crackers, in the descendants. The book begins by proving that any given descendant may be constructed by starting from a finite set of genes and introducing the required cubic crackers through the use of six special operations, called breeding operations. It shows that each breeding operation is invertible, and these inverse operations are examined. It is therefore possible, for any given descendant, to identify a family of genes that could be used to generate the descendant. The authors refer to such a family of genes as a “complete family of ancestor genes” for that particular descendant. The book proves the fundamental, although quite unexpected, result that any given descendant has exactly one complete family of ancestor genes. This result indicates that the particular combination of breeding operations used strikes the right balance between ensuring that every descendant may be constructed while permitting only one generating set. The result that any descendant can be constructed from a unique set of ancestor genes indicates that most of the structure in the descendant has been, in some way, inherited from that, very special, complete family of ancestor genes, with the remaining structure induced by the breeding operations. After establishing this, the authors proceed to investigate a number of graph theoretic properties: Hamiltonicity, bipartiteness, and planarity, and…
  table of contents: Genetic Theory for Cubic Graphs -- Inherited Properties of Descendants -- Uniqueness of Ancestor Genes -- Completed Proofs from Chapter 3.
  note: by Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe.
  subject:
    topic: Business
  subject:
    topic: Operations research
  subject:
    topic: Decision making
  subject:
    topic: Management science
  subject:
    topic: Graph theory
  subject:
    topic: Business and Management
  subject:
    topic: Operation Research/Decision Theory
  subject:
    topic: Operations Research, Management Science
  subject:
    topic: Graph Theory
  classification: HD30.23
  classification: 658.40301
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Operations Research
  identifier: 9783319196800
  identifier: http://dx.doi.org/10.1007/978-3-319-19680-0
  record info:
    record creation date: 150715
    record change date: 20151204191434.0
    record identifier: 978-3-319-19680-0