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Ptolemaic and Planar Cover-incomparability Graphs
Order ( IF 0.4 ) Pub Date : 2021-01-30 , DOI: 10.1007/s11083-021-09549-4 Arun Anil , Manoj Changat , Tanja Gologranc , Baiju Sukumaran
中文翻译:
托勒密和平面覆盖物不可比性图
更新日期:2021-01-31
Order ( IF 0.4 ) Pub Date : 2021-01-30 , DOI: 10.1007/s11083-021-09549-4 Arun Anil , Manoj Changat , Tanja Gologranc , Baiju Sukumaran
Cover-Incomparability graphs (C-I graphs) are graphs whose edge-set is the union of edge-sets of incomparability graph and the cover graph of some poset. We give a new characterization of Ptolemaic C-I graphs and prove that each C-I graph contains a Ptolemaic C-I graph as a spanning subgraph. This result is used to present several necessary conditions for a graph G being planar C-I graph. We present a hierarchy of subfamilies of chordal graphs in the class of C-I graphs and prove that many different graph families coincide in the class of C-I graphs.
中文翻译:
托勒密和平面覆盖物不可比性图
Cover-Incomparability图(CI图)是这样的图,其边集是不可比较图的边集与某些球的覆盖图的并集。我们给出了托勒密CI图的新特征,并证明每个CI图都包含一个托勒密CI图作为扩展子图。该结果用于表示图G为平面CI图的几个必要条件。我们在CI图类中提出了弦图子族的层次结构,并证明了在CI图类中许多不同的图族是重合的。