3-Restricted arc connectivity of digraphs
Lin, Shangwei1,2; Jin, Ya'nan1; Li, Chunfang1
AbstractThe k-restricted arc connectivity of digraphs is a common generalization of the arc connectivity and the restricted arc connectivity. An arc subset S of a strong digraph D is a k-restricted arc cut 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. The k-restricted arc connectivity lambda(k)(D) of a digraph D is the minimum cardinality over all k-restricted arc cuts of D. Let D be a strong digraph with order n >= 6 and minimum degree delta(D). In this paper, we first show that lambda(3)(D) exists if delta(D) >= 3 and, furthermore, lambda(3) (D) <= xi(3)(D) if delta(D) >= 4, where xi(3)(D) is the minimum 3-degree of D. Next, we prove that lambda(3)(D) = xi(3)(D) if delta(D) >= n+3/2 Finally, we give examples showing that these results are best possible in some sense. (C) 2017 Elsevier B.V. All rights reserved.
KeywordNetwork Digraph Connectivity Minimum degree
Funding ProjectNational Natural Science Foundation of China[61202017] ; Postdoctoral Science Foundation of China[2012M510579]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000407182200002
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Document Type期刊论文
Corresponding AuthorLin, Shangwei
Affiliation1.Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China
2.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Lin, Shangwei,Jin, Ya'nan,Li, Chunfang. 3-Restricted arc connectivity of digraphs[J]. DISCRETE MATHEMATICS,2017,340(10):2341-2348.
APA Lin, Shangwei,Jin, Ya'nan,&Li, Chunfang.(2017).3-Restricted arc connectivity of digraphs.DISCRETE MATHEMATICS,340(10),2341-2348.
MLA Lin, Shangwei,et al."3-Restricted arc connectivity of digraphs".DISCRETE MATHEMATICS 340.10(2017):2341-2348.
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