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The Resource Genetic theory for cubic graphs, Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe
Genetic theory for cubic graphs, Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe
Resource Information
The item Genetic theory for cubic graphs, Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Genetic theory for cubic graphs, Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
- Summary
- 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 prove results linking properties of the descendant to those of the ancestor genes. They develop necessary (and in some cases, sufficient) conditions for a descendant to contain a property in terms of the properties of its ancestor genes. These results motivate the development of parallelizable heuristics that first decompose a graph into ancestor genes, and then consider the genes individually. In particular, they provide such a heuristic for the Hamiltonian cycle problem. Additionally, a framework for constructing graphs with desired properties is developed, which shows how many (known) graphs that constitute counterexamples of conjectures could be easily found
- Language
- eng
- Extent
- 1 online resource.
- Contents
-
- Genetic Theory for Cubic Graphs
- Inherited Properties of Descendants
- Uniqueness of Ancestor Genes
- Completed Proofs from Chapter 3
- Isbn
- 9783319196800
- Label
- Genetic theory for cubic graphs
- Title
- Genetic theory for cubic graphs
- Statement of responsibility
- Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe
- Language
- eng
- Summary
- 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 prove results linking properties of the descendant to those of the ancestor genes. They develop necessary (and in some cases, sufficient) conditions for a descendant to contain a property in terms of the properties of its ancestor genes. These results motivate the development of parallelizable heuristics that first decompose a graph into ancestor genes, and then consider the genes individually. In particular, they provide such a heuristic for the Hamiltonian cycle problem. Additionally, a framework for constructing graphs with desired properties is developed, which shows how many (known) graphs that constitute counterexamples of conjectures could be easily found
- Cataloging source
- N$T
- http://library.link/vocab/creatorName
- Baniasadi, Pouya
- Dewey number
- 511.5
- Index
- index present
- LC call number
- QA166.243
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- bibliography
- http://library.link/vocab/relatedWorkOrContributorDate
- 1949-
- http://library.link/vocab/relatedWorkOrContributorName
-
- Ežov, Vladimir V.
- Filar, Jerzy A.
- Haythorpe, Michael
- Series statement
- Springer briefs in operations research
- http://library.link/vocab/subjectName
-
- Graph connectivity
- Graph theory
- MATHEMATICS
- Graph connectivity
- Graph theory
- Business and Management
- Operation Research/Decision Theory
- Operations Research, Management Science
- Graph Theory
- Operational research
- Combinatorics & graph theory
- Label
- Genetic theory for cubic graphs, Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- Genetic Theory for Cubic Graphs -- Inherited Properties of Descendants -- Uniqueness of Ancestor Genes -- Completed Proofs from Chapter 3
- Dimensions
- unknown
- Extent
- 1 online resource.
- File format
- unknown
- Form of item
- online
- Isbn
- 9783319196800
- Level of compression
- unknown
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Note
- SpringerLink
- Other control number
- 10.1007/978-3-319-19680-0
- Quality assurance targets
- not applicable
- Reformatting quality
- unknown
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
-
- (OCoLC)914165910
- (OCoLC)ocn914165910
- Label
- Genetic theory for cubic graphs, Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- Genetic Theory for Cubic Graphs -- Inherited Properties of Descendants -- Uniqueness of Ancestor Genes -- Completed Proofs from Chapter 3
- Dimensions
- unknown
- Extent
- 1 online resource.
- File format
- unknown
- Form of item
- online
- Isbn
- 9783319196800
- Level of compression
- unknown
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Note
- SpringerLink
- Other control number
- 10.1007/978-3-319-19680-0
- Quality assurance targets
- not applicable
- Reformatting quality
- unknown
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
-
- (OCoLC)914165910
- (OCoLC)ocn914165910
Library Locations
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Architecture LibraryBorrow itGould Hall 830 Van Vleet Oval Rm. 105, Norman, OK, 73019, US35.205706 -97.445050
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Chinese Literature Translation ArchiveBorrow it401 W. Brooks St., RM 414, Norman, OK, 73019, US35.207487 -97.447906
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Engineering LibraryBorrow itFelgar Hall 865 Asp Avenue, Rm. 222, Norman, OK, 73019, US35.205706 -97.445050
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Fine Arts LibraryBorrow itCatlett Music Center 500 West Boyd Street, Rm. 20, Norman, OK, 73019, US35.210371 -97.448244
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Harry W. Bass Business History CollectionBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 -97.447906
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History of Science CollectionsBorrow it401 W. Brooks St., Rm. 521NW, Norman, OK, 73019, US35.207487 -97.447906
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John and Mary Nichols Rare Books and Special CollectionsBorrow it401 W. Brooks St., Rm. 509NW, Norman, OK, 73019, US35.207487 -97.447906
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Price College Digital LibraryBorrow itAdams Hall 102 307 West Brooks St., Norman, OK, 73019, US35.210371 -97.448244
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Western History CollectionsBorrow itMonnet Hall 630 Parrington Oval, Rm. 300, Norman, OK, 73019, US35.209584 -97.445414
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/Genetic-theory-for-cubic-graphs-Pouya-Baniasadi/yfkDTnSdOzg/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/Genetic-theory-for-cubic-graphs-Pouya-Baniasadi/yfkDTnSdOzg/">Genetic theory for cubic graphs, Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>