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- W3196819477 abstract "For a graph G=(V,E) and a set S⊆V(G) of size at least 2, an S-Steiner tree T is a subgraph of G that is a tree with S⊆V(T). Two S-Steiner trees T and T′ are internally disjoint (resp. edge-disjoint) if E(T)∩E(T′)=∅ and V(T)∩V(T′)=S (resp. if E(T)∩E(T′)=∅). Let κG(S) (resp. λG(S)) denote the maximum number of internally disjoint (resp. edge-disjoint) S-Steiner trees in G. The k-tree connectivity κk(G) (resp. k-tree edge-connectivity λk(G)) of G is then defined as the minimum κG(S) (resp. λG(S)), where S ranges over all k-subsets of V(G). In Li et al. (2018) [12], the authors conjectured that if a connected graph G has at least k vertices and at least k edges, then κk(L(G))≥λk(G) for any k≥2, where L(G) is the line graph of G. In this paper, I confirm this conjecture and prove that the bound is sharp." @default.
- W3196819477 created "2021-09-13" @default.
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- W3196819477 date "2021-12-01" @default.
- W3196819477 modified "2023-10-16" @default.
- W3196819477 title "k-tree connectivity of line graphs" @default.
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- W3196819477 doi "https://doi.org/10.1016/j.disc.2021.112617" @default.
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