Signed B-edge Covers of Graphs
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چکیده
We study a signed variant of edge covers of graphs. Let b be a positive integer, and let G be a graph with minimum degree at least b. A signed b-edge cover of G is a function f : E(G) → {−1, 1} satisfying e∈EG(v) f(e) ≥ b for every v ∈ V (G). The minimum of the values of e∈E(G) f(e), taken over all signed b-edge covers f of G, is called the signed b-edge cover number and is denoted by ρb(G). For any positive integer b, we show that a minimum signed b-edge cover can be found in polynomial time, using a reduction to b-edge cover, which itself is solved by b-matching. A sharp lower bound for ρb and a sharp upper bound ρ2 are given. A sharp upper bound for ρ ′ b of Cartesian product graphs is presented. Exact values of ρb for cliques and bicliques are found.
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تاریخ انتشار 2007