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- W2200934108 abstract "Computing the span of subcubic graphs is NP-hard in the strong sense.It is polynomially solvable and approximable under some extra assumptions. Given a nonempty graph G and a function ? that assigns positive integers to the edges of G, a ?-coloring of G is a vertex coloring of G such that for every edge uv of G the colors assigned to the vertices u and v differ by at least ? ( u v ) . In the paper we study the problem of finding ?-colorings with minimal span, i.e. the difference between the largest and the smallest color used. We show that the problem, restricted to subcubic graphs, is:NP-hard in the strong sense but polynomially 3 2 -approximable for functions ? that take at most two values;polynomially 2-approximable and not ( 1 + e ) -approximable for any e < 1 2 , unless P = NP . We also show that, if we additionally assume that the edges that received the largest of the values of ? induce a spanning and connected subgraph, then it becomespolynomially 4 3 -approximable;polynomially solvable provided ? takes at most two values." @default.
- W2200934108 created "2016-06-24" @default.
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- W2200934108 date "2016-01-01" @default.
- W2200934108 modified "2023-09-25" @default.
- W2200934108 title "On the hardness of computing span of subcubic graphs" @default.
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- W2200934108 doi "https://doi.org/10.1016/j.ipl.2015.08.009" @default.
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