Given a graph G = (V; E);HCN(L(G)) is the minimum number of edges to be added to its line graph L(G) to make L(G) Hamiltonian. This problem is known to be NP-hard for general graphs, whereas a O(|V|) algorithm exists when G is a tree. In this paper a linear algorithm for finding HCN(L(G)) when G is a cactus is proposed.
Detti, P., Meloni, C. (2004). A linear algorithm for the Hamiltonian completion number of the line graph of a cactus. DISCRETE APPLIED MATHEMATICS, 136, 197-215 [10.1016/S0166-218X(03)00441-4].
A linear algorithm for the Hamiltonian completion number of the line graph of a cactus
DETTI, PAOLO;
2004-01-01
Abstract
Given a graph G = (V; E);HCN(L(G)) is the minimum number of edges to be added to its line graph L(G) to make L(G) Hamiltonian. This problem is known to be NP-hard for general graphs, whereas a O(|V|) algorithm exists when G is a tree. In this paper a linear algorithm for finding HCN(L(G)) when G is a cactus is proposed.
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https://hdl.handle.net/11365/3933
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