About: Thomassen's Conjecture Implies Polynomiality of 1-Hamilton-Connectedness in Line Graphs     Goto   Sponge   NotDistinct   Permalink

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  • A graph G is 1-Hamilton-connected if G?x is Hamilton-connected for every vertex x. We prove that Thomassen's conjecture (every 4-connected line graph is hamiltonian, or, equivalently, every snark has a dominating cycle) is equivalent to the statement that every 4-connected line graph is 1-Hamilton-connected. As a corollary, we obtain that Thomassen's conjecture implies polynomiality of 1-Hamilton-connectedness in line graphs. Consequently, proving that 1-Hamilton-connectedness is NP-complete in line graphs would disprove Thomassen's conjecture, unless P=NP
  • A graph G is 1-Hamilton-connected if G?x is Hamilton-connected for every vertex x. We prove that Thomassen's conjecture (every 4-connected line graph is hamiltonian, or, equivalently, every snark has a dominating cycle) is equivalent to the statement that every 4-connected line graph is 1-Hamilton-connected. As a corollary, we obtain that Thomassen's conjecture implies polynomiality of 1-Hamilton-connectedness in line graphs. Consequently, proving that 1-Hamilton-connectedness is NP-complete in line graphs would disprove Thomassen's conjecture, unless P=NP (en)
Title
  • Thomassen's Conjecture Implies Polynomiality of 1-Hamilton-Connectedness in Line Graphs
  • Thomassen's Conjecture Implies Polynomiality of 1-Hamilton-Connectedness in Line Graphs (en)
skos:prefLabel
  • Thomassen's Conjecture Implies Polynomiality of 1-Hamilton-Connectedness in Line Graphs
  • Thomassen's Conjecture Implies Polynomiality of 1-Hamilton-Connectedness in Line Graphs (en)
skos:notation
  • RIV/49777513:23520/12:43915022!RIV13-MSM-23520___
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  • P(1M0545), Z(MSM4977751301)
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  • 3
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  • 174366
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  • RIV/49777513:23520/12:43915022
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  • snark; Thomassen's conjecture; dominating cycle; Hamilton-connected; Hamiltonian; 4-connected; line graph (en)
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  • US - Spojené státy americké
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  • [E3BAACF08A58]
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  • Journal of Graph Theory
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  • 69
http://linked.open...iv/tvurceVysledku
  • Ryjáček, Zdeněk
  • Vrána, Petr
  • Kužel, Roman
http://linked.open...ain/vavai/riv/wos
  • 000300693600002
http://linked.open...n/vavai/riv/zamer
issn
  • 0364-9024
number of pages
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  • 10.1002/jgt.20578
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  • 23520
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