A graph G has the strong parity property if for every subset \(X\subseteq V(G)\) with |X| even, G has a spanning subgraph F with minimum degree at least one such that \(d_F(v)\equiv 1\pmod 2\) for all \(v\in X\), \(d_F(y)\equiv 0\pmod 2\) for all \(y\in V(G)-X\). Bujtás et al. (Graphs Combin 36(2020):1391–1399, 2020) introduced the concept and conjectured that every 2-edge-connected graph with minimum degree at least three has the strong parity property. In this paper, we give a characterization for graphs to have the strong parity property and construct a counterexample to disprove the conjecture proposed by Bujtás, Jendrol’ and Tuza.

如果对于每个具有| |的子集\（X \ subseteq V（G）\），则图G具有较强的奇偶性。X | 甚至，G都有一个最小度至少为1的生成子图F，使得所有\（v \ in X \），\（d_F（y）\ equiv 0的\ {d_F（v）\ equiv 1 \ pmod 2 \）\ pmod 2 \）全部\（y \ in V（G）-X \）。Bujtás等。（Graphs Combin 36（2020）：1391-1399，2020）引入了这一概念，并推测每个最小程度至少为3的2边连接图都具有很强的奇偶性。在本文中，我们对具有强奇偶性的图进行了刻画，并构造了一个反例来反驳Bujtás，Jendrol'和Tuza提出的猜想。