Introduction to Graph Theory · Problem 5.12

Trees and arborescences — Darij Grinberg

Mathematics — Graph Theory · distances-multigraph

Problem

Let

a

b

and

c

be three vertices of a connected multigraph

G = (V, E, \varphi)

. Prove that

d(b,c) + d(c,a) + d(a,b) \leq 2|V| - 2