A solution to a conjecture on the generalized connectivity of graphs

Lily Chen (), Xueliang Li (), Mengmeng Liu () and Yaping Mao ()
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Lily Chen: Huaqiao University
Xueliang Li: Nankai University
Mengmeng Liu: Nankai University
Yaping Mao: Nankai University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 1, No 19, 275-282

Abstract: Abstract The generalized k-connectivity $$\kappa _k(G)$$ κ k ( G ) of a graph G was introduced by Chartrand et al. in (Bull Bombay Math Colloq 2:1–6, 1984), which is a nice generalization of the classical connectivity. Recently, as a natural counterpart, Li et al. proposed the concept of generalized edge-connectivity for a graph. In this paper, we consider the computational complexity of the generalized connectivity and generalized edge-connectivity of a graph. We give a confirmative solution to a conjecture raised by S. Li in Ph.D. Thesis (2012). We also give a polynomial-time algorithm to a problem of generalized k-edge-connectivity.

Keywords: Generalized connectivity; Generalized edge-connectivity; Complexity; Polynomial-time algorithm; $$\mathcal {N}\mathcal {P}$$ N P -complete; 05C40; 05C05; 68Q25; 68R10 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10878-015-9955-x

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