On Efficient Construction of MinimumSum Vertex Covers
Abstract
Let G = ( V, E) be a simple graph. A vertex labeling is a bijection f: V → { l, 2, ... ,!VI}. The
weight w(e) of an edge e = uv ∈E is given by w(e) = min{f(u), f(v)}. The minimumsum ver~ex
cover is a vertex labeling that minimizes ∑ₑ∈ ᴇ ʷ(ͤ) . The minimum such sum is called the min~mumsum
vertex cover cost, denoted by µ (G). The problem of determining µs (G) is NPcomplete
m the general case, however, we show that minimumsum vertex covers of split graphs and caterpillars
can be computed in polynomial time.
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