A linear algorithm for the Hamiltonian completion number of the line graph of a cactus

Authors:
Paolo Detti;Carlo Meloni
Affiliations:
Dipartimento di Ingegneria dell' Informazione, Università di Siena, Via Roma, 56, 1-53100 Siena, Italy;Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, Via E. Orabona, 4 I-70125, Bari, Italy
Venue:
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Year:
2004

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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.