Hyperbolicity in Median Graphs

Proceedings Mathematical Sciences

José M Sigarreta¹ 

[1] Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No. Col. Garita, 0 Acalpulco Gro., Mexico$$

关键词: Median graph;    Gromov hyperbolicity;    Gromov hyperbolic graph;    infinite graphs;    geodesics.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

If 𝑋 is a geodesic metric space and $x_1,x_2,x_3in X$, a geodesic triangle $T={x_1,x_2,x_3}$ is the union of the three geodesics $[x_1 x_2],[x_2 x_3]$ and $[x_3 x_1]$ in 𝑋. The space 𝑋 is 𝛿-hyperbolic (in the Gromov sense) if any side of 𝑇 is contained in a 𝛿-neighborhood of the union of the two other sides, for every geodesic triangle 𝑇 in 𝑋. If 𝑋 is hyperbolic, we denote by 𝛿(𝑋) the sharp hyperbolicity constant of 𝑋, i.e.,$𝛿(X)=inf{𝛿≥ 0: X quadext{is}quad 𝛿-ext{hyperbolic}}$. In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its bigons are thin.

【 授权许可】

Unknown