On the independence number in subcubic graphs
Abstract
For a connected subcubic graph G≠ K1 let Vi(G) = \v ∈ V(G) ~|~ dG(v)=i\ for 1 ≤ i ≤ 3. Given c1, c2, c 3 ∈ R+ and d ∈ R, we show several results of type α(G) ≥ c1|V1(G)| + c2|V2(G)| + c3|V3(G)| - d. We also derive classes of graphs G showing sharpness of these lower bounds on the independence number α(G) of G.
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