<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:math>-Optimality of Bipartite Digraphs

Chen, Xing; Liu, Juan; Meng, Jixiang

doi:10.1016/j.ipl.2012.05.003

Cited by 5 publications

(1 citation statement)

References 16 publications

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“…In [11], Hellwig and Volkmann concluded many sufficient conditions for digraphs to be λ-optimal. Besides, sufficient conditions for digraphs to be λ ′ -optimal were also given by several authors, for example by Balbuena et al [1][2][3][4], Chen et al [5,6], Grüter and Guo [7,8], Liu and Zhang [9], Volkmann [12] and Wang and Lin [13]. However, closely related conditions for λ 3 -optimal digraphs have received little attention until recently.…”

Section: Introductionmentioning

confidence: 99%

On the optimality of 3-restricted arc connectivity for digraphs and bipartite digraphs

Zhang¹,

Meng²

2022

Discuss. Math. Graph Theory

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Let D be a strong digraph. An arc subset S is a k-restricted arc cut of D if D − S has a strong component D ′ with order at least k such that D\V (D ′) contains a connected subdigraph with order at least k. If such a k-restricted arc cut exists in D, then D is called λ k-connected. For a λ kconnected digraph D, the k-restricted arc connectivity, denoted by λ k (D), is the minimum cardinality over all k-restricted arc cuts of D. It is known that for many digraphs λ k (D) ≤ ξ k (D), where ξ k (D) denotes the minimum k-degree of D. D is called λ k-optimal if λ k (D) = ξ k (D). In this paper, we will give some sufficient conditions for digraphs and bipartite digraphs to be λ 3-optimal.

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Section: Introductionmentioning

confidence: 99%

On the optimality of 3-restricted arc connectivity for digraphs and bipartite digraphs

Zhang¹,

Meng²

2022

Discuss. Math. Graph Theory

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Bounds on the k-restricted arc connectivity of some bipartite tournaments

Balbuena

González-Moreno

Olsen

2018

Applied Mathematics and Computation

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For k ≥ 2, a strongly connected digraph D is called λ k-connected if it contains a set of arcs W such that D − W contains at least k non-trivial strong components. The krestricted arc connectivity of a digraph D was defined by Volkmann as λ k (D) = min {| W | : W is a k-restricted arc-cut }. In this paper we bound λ k (T) for a family of bipartite tournaments T called projective bipartite tournaments. We also introduce a family of "good" bipartite oriented digraphs. For a good bipartite tournament T we prove that if the minimum degree of T is at least 1. 5 k − 1 then k (k − 1) ≤ λ k (T) ≤ k (N − 2 k − 2) , where N is the order of the tournament. As a consequence, we derive better bounds for circulant bipartite tournaments.

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3-Restricted arc connectivity of digraphs

Lin

Jin

2017

Discrete Mathematics

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λ′-Optimality of Bipartite Digraphs

Cited by 5 publications

References 16 publications

On the optimality of 3-restricted arc connectivity for digraphs and bipartite digraphs

On the optimality of 3-restricted arc connectivity for digraphs and bipartite digraphs

Bounds on the k-restricted arc connectivity of some bipartite tournaments

3-Restricted arc connectivity of digraphs

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