论文标题
分数强制图数
Fractional forcing number of graphs
论文作者
论文摘要
Harary，Klein和Živković引入了强迫进行完美比赛的概念。该问题在化学中的应用及其有趣的理论方面使该主题非常活跃。在这项工作中，我们介绍了强迫分数完美匹配的函数的概念，该匹配与强迫在完美匹配的图形上定义的集合相似。我们表明，此对象是积分强制集的连续凹形函数扩展。然后，我们在连续的世界中使用结果来结束新的界限，并在强迫集的离散情况下，为常规边缘传输图的家族而言。特别是，我们得出了新的上限，以最大程度地强迫图形图。
The notion of forcing sets for perfect matchings was introduced by Harary, Klein, and Živković. The application of this problem in chemistry, as well as its interesting theoretical aspects, made this subject very active. In this work, we introduce the notion of forcing function of fractional perfect matchings, which is continuous analogous to forcing sets defined over the perfect matching polytope of graphs. We show that this object is a continuous and concave function extension of the integral forcing set. Then, we use our results in the continuous world to conclude new bounds and results in the discrete case of forcing sets, for the family of regular edge-transitive graphs. In particular, we derive new upper bounds for the maximum forcing number of hypercube graphs.
