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- W2088654300 abstract "A k - container of G between u and v , C ( u , v ) , is a set of k internally disjoint paths between u and v . A k ∗ - container C ( u , v ) of G is a k -container if it contains all vertices of G . A graph G is k ∗ - connected if there exists a k ∗ -container between any two distinct vertices. Thus, every 1 ∗ -connected graph is Hamiltonian connected. Moreover, every 2 ∗ -connected graph is Hamiltonian. Zhan proved that G = L ( M ) is Hamiltonian connected if the edge-connectivity of M is at least 4. In this paper, we generalize this result by proving G = L ( M ) is k ∗ -connected if the edge-connectivity of M is at least max { 2 k , 4 } . We also generalize our result into spanning fan-connectivity." @default.
- W2088654300 created "2016-06-24" @default.
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- W2088654300 date "2011-09-01" @default.
- W2088654300 modified "2023-09-27" @default.
- W2088654300 title "The spanning connectivity of line graphs" @default.
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- W2088654300 doi "https://doi.org/10.1016/j.aml.2011.04.013" @default.
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