Forcing on Perfect Matchings - A Survey
Forcing on Perfect Matchings - A Survey
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发表时间：
2011
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通讯作者：
Zhongyuan Che;Zhibo Chen
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作者：
Zhongyuan Che;Zhibo Chen
强迫边和强迫完美匹配数的概念最早出现在Harary，Klein等人1991年的一篇论文中。这些概念的根源可以追溯到Randic和Klein在1985- 1987年的著作（（24）和（36））中，其中以凯库勒结构的“固有自由度”的名义引入了强迫数，它在化学共振理论中起着重要作用。近二十年来，越来越多的数学家开始关注关于强迫集（包括强迫边、强迫面等）的研究。以及图的完美匹配的强迫数。图的研究范围已经从多边形扩展到各种二部图和非二部图。近年来，全球强迫匹配和反强迫匹配等问题也不断涌现.在此，我们将对这一新兴领域中的一些已知结果以及一些未解决的问题和猜想进行简要的综述。
The notions of a forcing edge and the forcing number of a perfect matching first appeared in a 1991 paper (15) by Harary, Klein andc. The root of these concepts can be traced to the works ((24) and (36)) by Randic and Klein in 1985- 1987, where the forcing number was introduced under the name of "innate degree of freedom" of a Kekule structure, which plays an important role in the resonance theory in chemistry. Over the past two decades, more and more mathematicians were attracted to the study on forcing sets (including forcing edges and forcing faces, etc.) and the forcing numbers of perfect matchings of a graph. The scope of graphs in consideration has been extended from polyhexes to various bipartite graphs and non-bipartite graphs. Some varied topics such as global forcing matchings and anti- forcing matchings also emerged recently. Here we will present a brief survey on the known results, as well as some open problems and conjectures in this growing field.