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A binary vertex coloring (labeling) f : V (G) → Z 2 of a graph G is said to be friendly if the number of vertices labeled 0 is almost the same as the number of vertices labeled 1. This friendly labeling induces an edge labeling f * : E(G) → Z 2 defined by f * (uv) = f (u)f (v) for all uv ∈ E(G). Let e f (i) = |{uv ∈ E(G) : f * (uv) = i}| be the number of… (More)

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