  The determination of 1-factorizations $F$ of girth-regular graphs of girth,
regular degree and chromatic index $g$ is undertaken for the cases in which
each girth cycle intersects every 1-factor of $F$, for $g\in\{3,4,5,6\}$. This
endeavor may apply to priority assignment problems, managerial situations in
optimization and decision making. Applications to hamiltonian decomposability
(via union of pairs of 1-factors) and to 3-dimensional geometry (M\"obius-strip
compounds and hollow-triangle polylinks) are given.
