On edge connectivity and parity factor (Q2353240)

This paper considers some sufficient conditions for a graph to have an even and even factor with restricted minimum degree and edge connectivity. In particular, the authors prove that every \(n\)-edge-connected graph with minimum degree at least \(n+1\) contains an even factor with minimum degree at least \(n\), and very \((m+1)\)-edge-connected graph contains an odd factor with minimum degree at least m, where n is even and m is odd. The results are shown to be best possible.