About: Stability of Hereditary Graph Classes Under Closure Operations     Goto   Sponge   NotDistinct   Permalink

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  • If C is a subclass of the class of claw-free graphs, then C is said to be stable if, for any graph G from C, the local completion of G at any vertex is also in C. If cl is a closure operation that turns a claw-free graph into a line graph by a series of local completions and C is stable, then cl(G) belongs to C for any graph G from C. We consider stability of hereditary classes of claw-free graphs defined in terms of a family of connected closed forbidden induced subgraphs. We characterize line graph preimages of graphs in families that yield stable classes, we identify minimal families that yield stable classes in the finite case, and we also give a general background for techniques for handling unstable induced hereditary classes by proving that their closure may be included into another (possibly stable) class.
  • If C is a subclass of the class of claw-free graphs, then C is said to be stable if, for any graph G from C, the local completion of G at any vertex is also in C. If cl is a closure operation that turns a claw-free graph into a line graph by a series of local completions and C is stable, then cl(G) belongs to C for any graph G from C. We consider stability of hereditary classes of claw-free graphs defined in terms of a family of connected closed forbidden induced subgraphs. We characterize line graph preimages of graphs in families that yield stable classes, we identify minimal families that yield stable classes in the finite case, and we also give a general background for techniques for handling unstable induced hereditary classes by proving that their closure may be included into another (possibly stable) class. (en)
Title
  • Stability of Hereditary Graph Classes Under Closure Operations
  • Stability of Hereditary Graph Classes Under Closure Operations (en)
skos:prefLabel
  • Stability of Hereditary Graph Classes Under Closure Operations
  • Stability of Hereditary Graph Classes Under Closure Operations (en)
skos:notation
  • RIV/49777513:23520/13:43918750!RIV14-MSM-23520___
http://linked.open...avai/predkladatel
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  • P(1M0545), Z(MSM4977751301)
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  • 1
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  • 107384
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  • RIV/49777513:23520/13:43918750
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  • stable class; closure; forbidden subgraph; hereditary class (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [2C83B547B38E]
http://linked.open...i/riv/nazevZdroje
  • Journal of Graph Theory
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  • 74
http://linked.open...iv/tvurceVysledku
  • Ryan, Joe
  • Ryjáček, Zdeněk
  • Vrána, Petr
  • Teska, Jakub
  • Miller, Miroslava
http://linked.open...n/vavai/riv/zamer
issn
  • 0364-9024
number of pages
http://bibframe.org/vocab/doi
  • 10.1002/jgt.21692
http://localhost/t...ganizacniJednotka
  • 23520
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