10-Gabriel graphs are Hamiltonian

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F15%3A43925890" target="_blank" >RIV/49777513:23520/15:43925890 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ipl.2015.05.013" target="_blank" >http://dx.doi.org/10.1016/j.ipl.2015.05.013</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ipl.2015.05.013" target="_blank" >10.1016/j.ipl.2015.05.013</a>

Result language
angličtina
Original language name
10-Gabriel graphs are Hamiltonian
Original language description
Given a set S of points in the plane, the k-Gabriel graph of S is the geometric graph with vertex set S, where two points x,y in S are connected by an edge if and only if the closed disk having segment xy as diameter contains at most k points of S otherthan x and y. We consider the following question: What is the minimum value of k such that the k-Gabriel graph of every point set S contains a Hamiltonian cycle? For this value, we give an upper bound of 10 and a lower bound of 2. The best previously known values were 15 and 1, respectively.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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