Characterization of Gromov Hyperbolic Short Graphs

作     者：José Manuel RODRIGUEZ 

作者机构：Departamento de MatemticasUniversidad Carlos III de MadridAvenida de la Universidad 30 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2014年第30卷第2期

页      面：197-212页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by Ministerio de Ciencia e Innovación of Spain(Grant No.MTM 2009-07800) a grant from Consejo Nacional De Ciencia Y Tecnologia of México(Grant No.CONACYT-UAG I0110/62/10) 

主　　题：Short graph Gromov hyperbolicity Gromov hyperbolic graph infinite graphs geodesics 

摘      要：To decide when a graph is Gromov hyperbolic is,in general,a very hard problem.In this paper,we solve this problem for the set of short graphs（in an informal way,a graph G is r-short if the shortcuts in the cycles of G have length less than r）：an r-short graph G is hyperbolic if and only if S9r（G）is finite,where SR（G）：=sup{L（C）：C is an R-isometric cycle in G}and we say that a cycle C is R-isometric if dC（x,y）≤dG（x,y）＋R for every x,y∈C.