|Title:||Optimal Covering of Cacti By Vertex-Disjoint Paths
|Authors:||Shlomo Moran and Yaron Wolfstahl
|Abstract:||A path cover (abbv. cover) of a graph G is a set of vertex-disjoint paths which cover all the vertices of G. An optimal cover of G is a cover of the minimum possible cardinality. The optimal covering problem is known to be NP-complete even for cubic 3-connected planar graphs where no face has fewer than 5 edges. Motivated by the intractability of this problem, we develop an efficient optimal covering algorithm for cacti (i.e. graphs where no edge lies on more than one cycle). In doing so we generalize the result of  and , where optimal covering algorithms for trees and graphs where no two cycles share a vertex were presented.|
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