Thomassen's Conjecture Implies Polynomiality of 1-Hamilton-Connectedness in Line Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F12%3A43915022" target="_blank" >RIV/49777513:23520/12:43915022 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/jgt.20578" target="_blank" >http://dx.doi.org/10.1002/jgt.20578</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.20578" target="_blank" >10.1002/jgt.20578</a>

Result language
angličtina
Original language name
Thomassen's Conjecture Implies Polynomiality of 1-Hamilton-Connectedness in Line Graphs
Original language description
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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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