Long cycles in hypercubes with optimal number of faulty vertices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10103308" target="_blank" >RIV/00216208:11320/12:10103308 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10878-011-9379-1" target="_blank" >http://dx.doi.org/10.1007/s10878-011-9379-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10878-011-9379-1" target="_blank" >10.1007/s10878-011-9379-1</a>

Result language
angličtina
Original language name
Long cycles in hypercubes with optimal number of faulty vertices
Original language description
We prove a conjecture of Castaneda and Gotchev that for every set F of at most n(n-1)/2 vertices, the hypercube of dimension n contains a cycle of length at least 2^n-2|F| that avoids F. We also prove that for every set F of at most (n^2+n-4)/4 vertices,the hypercube of dimension n contains a path of length at least 2n-2|F|-2 between any two vertices such that each of them has at most 3 neighbors in F. We introduce a new technique of potentials which could be of independent interest.
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
IN - Informatics
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)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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

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