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Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced amethod to construct a manifold decomposition of double branched cover of (S3,k) from a thin position of k. In this article, we will prove that if a thinposition of k induces a thin decomposition of double branched cover of (S3,k)by Howards and Schultens' method, then the thin position is the sum of primesummands by stacking a thin position of one of prime summands of k on top of athin position of another prime summand, and so on. Therefore, k holds thenearly additivity of knot width (i.e. for k = k1#k2, w(k) = w(k1)#w(k2) - 2) inthis case. Moreover, we will generalize the hypothesis to the property a thinposition induces a manifold decomposition whose thick surfaces consists ofstrongly irreducible or critical surfaces (so topologically minimal.)

A note on the nearly additivity of knot width