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 ...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.展开更多
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)
文摘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.
