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Diskretnyi Analiz i Issledovanie Operatsii, Ser. 1, 2006, Volume 13, Issue 1, Pages 99–108
(Mi da26)
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This article is cited in 7 scientific papers (total in 7 papers)
Sufficient conditions for the existence of a graph with a given variety of balls
K. L. Rychkov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
It is proved that for each positive integer $d$ and each collection of integers $\overline\tau=(\tau_0,\tau_1,\dots,\tau_d)$ such that $\tau_0\geqslant\tau_1\geqslant\dots\geqslant\tau_d=1$ and $\tau_{d-1}\geqslant d^2+1$, there exists a graph of diameter $d$ whose variety vector of the balls is equal to $\overline\tau$; if $d\geqslant 3$ then there is no graph of diameter $d$ whose variety vector of balls $(\tau_0,\tau_1,\dots,\tau_d)$ satisfies the condition $\tau_0=\tau_1=\dots=\tau_{d-1}\leqslant2d-1$.
Received: 27.10.2005
Citation:
K. L. Rychkov, “Sufficient conditions for the existence of a graph with a given variety of balls”, Diskretn. Anal. Issled. Oper., Ser. 1, 13:1 (2006), 99–108; J. Appl. Industr. Math., 1:3 (2007), 380–385
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Abstract page: | 471 | Full-text PDF : | 101 | References: | 66 |
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