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A CHARACTERIZATION OF THE EMBEDDABILITY OF GRAPHS ON THE SURFACE OF GIVEN GENUS
作者姓名:Liu Ying  Liu Yanpei
作者单位:Liu Ying * Liu Yanpei * *Institute of Applied Mathematics,Chinese Academy of Sciences,100080,Beijing,China
摘    要:§1.IntroductionThesymbolsandthetechnicaltermsnotexplainedinthispapercanbefoundin1]and3].AgraphisoftendenotedbyG=(V,E),υ=|V|andε=|E|arecalleditsorderandsizerespectively.IthasbeenshownbyR.Duke4]thatifaconnectedgraphGhasembeddings(or2-cellembeddingsinDuke’stermi…

关 键 词:双曲线图  欧拉直接回路  可定向曲面  嵌入性
收稿时间:1994/3/30 0:00:00
修稿时间:1994/12/5 0:00:00

A CHARACTERIZATION OF THE EMBEDDABILITY OF GRAPHS ON THE SURFACE OF GIVEN GENUS
Liu Ying,Liu Yanpei.A CHARACTERIZATION OF THE EMBEDDABILITY OF GRAPHS ON THE SURFACE OF GIVEN GENUS[J].Chinese Annals of Mathematics,Series B,1996,17(4):457-462.
Authors:Liu Ying and Liu Yanpei
Institution:InstituteofAppliedMathemtics,ChineseAcademyofSciences,100080,BeijingChina.
Abstract:The embedding technique based on an operator appeared in Liu, Y. P., Scientia Sinica, Special Issue on Math,1 (1979),191-201 (in Chinese)] for determining the maximum non-orientable genus of a graph is developed to obtain the general theorem which presents a necessary and sufficient condition for a graph to be embeddable into either the orientable or the non-orientable surface of genus k. Furthermore,the greatest lower bound of the lengths of genus ranges of the class of nonplanar graphs which are up-embeddable is also obtained.
Keywords:Double graph  Eulerian directed circuit  Orientable surface  Embeddability
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