Biregular subgraphs of biregular graphs (Q1091405)

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 \(0\leq r\leq k\). This result is the best possible in the sense that a family of biregular graphs whose degrees are either \(\delta\) or \(\delta +k\) (\(\delta\geq 2\), \(k\geq 2)\) has been found with the property that they do not contain a spanning biregular subgraph whose degrees are either \(\delta\)-1 or \(\delta\).