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- W2021962931 abstract "An acyclic graphoidal cover of a graph G is a collection ψ of paths in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ and every edge of G is in exactly one path in ψ. The minimum cardinality of an acyclic graphoidal cover of G is called the acyclic graphoidal covering number of G and is denoted by η a . A path partition of a graph G is a collection P of paths in G such that every edge of G is in exactly one path in P. The minimum cardinality of a path partition of G is called the path partition number of G and is denoted by π. In this paper we determine η a and π for several classes of graphs and obtain a characterization of all graphs with Δ ⩽ 4 and η a = Δ − 1. We also obtain a characterization of all graphs for which η a = π." @default.
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- W2021962931 title "Acyclic graphoidal covers and path partitions in a graph" @default.
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- W2021962931 doi "https://doi.org/10.1016/s0012-365x(98)00032-6" @default.
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