Abstract
This paper deals with constrained cycle cover problem in Halin graphs. A (constrained) cycle cover of a graph is a set of cycles such that every (selected) vertex is in at least one cycle. This problem arises in the design fiber-optic telecommunication networks which employ a set of rings covering the network. Besides two types of minimum weight cycle cover problem, we also settle the problem of covering Halin graphs with an optimal 2-edge-connected subgraph. Linear time algorithms are given for all of the problems.
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