Abstract
The following theorem is proved: Every biregular graph whose degrees are either k or k + 1 contains a spanning biregular subgraph whose degrees are either r or r + 1 where 0⩽ r⩽ k. This result is the best possible in the sense that a family of biregular graphs whose degrees are either δ or δ + k ( δ⩾2, k⩾2) has been found with the property that they do not contain a spanning biregular subgraph whose degrees are either δ − 1 or δ.
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