期刊名称：International Journal of Innovative Research in Science, Engineering and Technology
印刷版ISSN：2347-6710
电子版ISSN：2319-8753
出版年度：2014
卷号：3
期号：12
页码：18101
DOI：10.15680/IJIRSET.2014.0312113
出版社：S&S Publications
摘要：Kuratowski's Theorem, perhaps the most famous result in graph theory, states that K5 and K3,3 are theonly non-planar graphs for which both G\e, the deletion of the edge e, and G/e, the contraction of the edge e, are planarfor all edges e of G. We characterize the planar graphs edge series, those non-planar graphs for which G\e or G/e isplanar for all edges e of G. This paper gives five characterizations of the planar graphs: an explicit description of thestructure of planar graphs; and an excluded minor criterion. We also give a best possible bound on the number of edgesof anplanar graph.
