Metadata language
Title:
On Hamiltonian Bypasses in one Class of HamiltonianDigraphs ; О гамильтоновых обходах в одном классегамильтоновых орграфов
Author:
Darbinyan Samvel ; Karapetyan Iskandar ; Дарбинян Самвел ; Карапетян Искандар
Type:
Uncontrolled Keywords:
Digraphs ; Cycles ; Hamiltonian cycles ; Hamiltonian bypasses
Abstract:
Let D be a strongly connected directed graph of order n > 4 which satisfies the following condition (*): for every pair of non-adjacent vertices x,y with a common in-neighbour d(x) + d(y) > 2n — 1 and minfd(x), d(y)g > n — 1. In [2] (J. of Graph Theory 22 (2) (1996) 181-187)) J. Bang-Jensen, G. Gutin and H. Li proved that D is Hamiltonian. In [9] it was shown that if D satisfies the condition (*) and the minimum semi-degree of D at least two, then either D contains a pre-Hamiltonian cycle (i.e., a cycle of length n — 1) or n is even and D is isomorphic to complete bipartite digraph (or to complete bipartite digraph minus one arc) with equal partite sets. In this paper we show that if the minimum out-degree of D at least two and the minimum in-degree of D at least three, then D contains also a Hamiltonian bypass, (i.e., a subdigraph is obtained from a Hamiltonian cycle by reversing exactly one arc).
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Доказывается, что любой сильно связный n -вершинный (n > 3) ор гр аф , который удовлетворяе т одному достаточному условию гамильтоновости орграфов (J.of Graph Theory 22(2) (1996) 181-187) и имеет минимальную полустепень исхода и зах од а не меншье чем 2 и 3, соотве тственно, содежит гамильтоновый обход, т.е., контур, который получается из гамильтонового контура после переориентации одной дуги.
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Date accepted:
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Journal or Publication Title:
Mathematical Problems of Computer Science
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Additional Information:
isko@ipia.sci.am ; samdarbin@ipia.sci.am
Affiliation:
Institute for Informatics and Automation Problems