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This paper addresses, in the context of wireless network design, the problem of optimally partitioning the spectrum into a set of nonoverlapping channels with nonuniform spectrum widths. While narrower bands split the total available spectrum into more nonoverlapping channels allowing more parallel concurrent transmissions, wider spectrum bands yield links with larger transport capacity. Thus, we model the combinatorially complex problem of joint routing, link scheduling, and variable-width channel allocation in both single and multirate multihop wireless networks as a mixed integer linear program, and present a solution framework using the column generation decomposition approach. Given the nature and complexity of the resulting dual subproblem, we propose heuristic methods for partitioning the spectrum and allocating resources to each active links, and hence obtain solutions for larger network instances. We present several numerical results and engineering insights suggesting both spectrum width and transmission rates as effective tunable knobs for combatting interference and promoting spatial reuse and thus achieving superior performance in multihop settings.