Prikladnaya Diskretnaya Matematika. Supplement
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Prikladnaya Diskretnaya Matematika. Supplement, 2017, Issue 10, Pages 134–136
DOI: https://doi.org/10.17223/2226308X/10/52
(Mi pdma347)
 

Applied Theory of Coding, Automata and Graphs

Upper and lower bounds of the number of additional arcs in a minimal edge $1$-extension of oriented path

M. B. Abrosimova, O. V. Modenovab

a Saratov State University, Saratov
b Saratov
References:
Abstract: The following upper and lower bounds of the number of additional arcs $ec(P_n)$ in a minimal edge $1$-extension of an oriented path $P_n$ are obtained: 1) for $P_n$ which has ends of different types and is not isomorphic to Hamiltonian path or to orientation consisting of alternating sources and sinks, $\lceil n/6\rceil+1\leq ec(P_n)\leq n+1$; 2) for $P_n$ with ends of equal types, $\lceil n/4\rceil+1\leq ec(P_n)\leq n+1$.
Keywords: minimal edge extension, path orientation, fault-tolerance.
Document Type: Article
UDC: 519.17
Language: Russian
Citation: M. B. Abrosimov, O. V. Modenova, “Upper and lower bounds of the number of additional arcs in a minimal edge $1$-extension of oriented path”, Prikl. Diskr. Mat. Suppl., 2017, no. 10, 134–136
Citation in format AMSBIB
\Bibitem{AbrMod17}
\by M.~B.~Abrosimov, O.~V.~Modenova
\paper Upper and lower bounds of the number of additional arcs in a~minimal edge $1$-extension of oriented path
\jour Prikl. Diskr. Mat. Suppl.
\yr 2017
\issue 10
\pages 134--136
\mathnet{http://mi.mathnet.ru/pdma347}
\crossref{https://doi.org/10.17223/2226308X/10/52}
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