论文标题
具有强大平价因子的图表的表征
A characterization for graphs having strong parity factors
论文作者
论文摘要
如果每个子集$ x \ subseteq v $ agragh $ g $具有\ emph {stront Parity propert}，则带有$ | x | $偶数，$ g $，$ g $具有至少一个，至少一个，以至于$ d_f（v）\ equiv 1 \ equiv 1 \ equiv 1 \ pmod for x $ in x $，$ d_ $，$ d_ $ quiv（$ d _ quiv（$ d_） v（g）-x $。 Bujtás，Jendrol和Tuza（关于图形的特定因素，\ Emph {Graphs and Combin。}，36（2020），1391-1399。）引入了概念，并推测，每个2-边缘的图形至少具有最小的图形至少三个具有三个具有强度的属性。在本文中，我们给出了图表的特征，使其具有强大的奇偶校验特性，并构建一个反例，以反驳Bujtás，Jendrol和Tuza提出的猜想。
A graph $G$ has the \emph{strong parity property} if for every subset $X\subseteq V$ 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, Jendrol and Tuza (On specific factors in graphs, \emph{Graphs and Combin.}, 36 (2020), 1391-1399.) 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.
