k-tree connectivity of line graphs

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چکیده

For a graph G = ( V , E ) and set S ⊆ of size at least 2, an S-Steiner tree T is subgraph that with . Two -Steiner trees ′ are internally disjoint (resp. edge-disjoint if ∩ ∅ ). Let κ λ denote the maximum number edge-disjoint) in The k-tree connectivity k edge-connectivity then defined as minimum ), where ranges over all -subsets In Li et al. (2018) [12] authors conjectured connected has vertices edges, L ≥ for any 2 line this paper, I confirm conjecture prove bound sharp.

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2021

ISSN: ['1872-681X', '0012-365X']

DOI: https://doi.org/10.1016/j.disc.2021.112617