2-edge-Hamiltonian-connectedness of 4-connected plane graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F14%3A43920431" target="_blank" >RIV/49777513:23520/14:43920431 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ejc.2013.06.033" target="_blank" >http://dx.doi.org/10.1016/j.ejc.2013.06.033</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2013.06.033" target="_blank" >10.1016/j.ejc.2013.06.033</a>

Result language
angličtina
Original language name
2-edge-Hamiltonian-connectedness of 4-connected plane graphs
Original language description
A graph G is called 2-edge-Hamiltonian-connect,ed if for every two edges e,f, G has a Hamiltonian cycle containing the edges e,f. In this paper, we show that every 4-connected plane graph is 2-edge-Hamiltonian-connected. This result is best possible in many senses and an extension of several known results on Hamiltonicity of 4-connected plane graphs, for example, Tutte`s result saying that every 4-connected plane graph is Hamiltonian, and Thomassen`s result saying that every 4-connected plane graph is Hamiltonian-connected. We also show that although the problem of deciding whether a given graph is 2-edge-Hamiltonian-connected is NP-complete, there exists a polynomial time algorithm to solve the problem if we restrict the input to plane graphs.
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/ED1.1.00%2F02.0090" target="_blank" >ED1.1.00/02.0090: NTIS - New Technologies for Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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