A tree R such that after deleting all leaves we obtain a path P is called a caterpillar. The path P is called the spine of the caterpillar R. If the spine has length 3 and R on 2n vertices contains vertices of degrees r, s, t, 2, where 2 < r, s, t < n, then we say that R is an [r, s, t, 2]-caterpillar of diameter 5. We completely characterize [r, s, t, 2]-caterpillars of diameter 5 on 4k + 2 vertices that factorize the complete graph K_(4k+2).
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