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Cover for path
Given a directed graph G, the minimum path cover problem consists of finding a path cover for G having the least number of paths. A minimum path cover consists of one path if and only if there is a Hamiltonian path in G. The Hamiltonian path problem is NP-complete, and hence the minimum path cover problem is NP-hard. Definition () A path cover of a graph G is a collection ψ of paths in G such that every edge of G is in exactly one path in ψ. The minimum cardinality of a path cover of G is called the path covering number of G and is denoted by π(G) or simply π. In particular, we derive the optimal size of an identifying path cover for paths, we show that any connected graph G has an identifying path cover of size at most .
of vertex disjoint paths that cover V (i.e., every vertex of G is in exactly one Key words. cocomparability graphs, minimum path cover problem. Abstract. A minimum Hamiltonian completion of a graph G is a minimum-size set of edges that, when added to G, guarantee a Hamiltonian path. Finding a. We study two restricted versions of the Subforest Isomorphism problem, the Star- Cover of a Tree (SCT) and the Path-Cover of a Tree(PCT) problems.
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