Introduction to Graph Theory · Problem 5.14

Trees and arborescences — Darij Grinberg

Mathematics — Graph Theory · four-point-condition-trees

Problem

Let

G

be a tree. Let

x

y

z

and

w

be four vertices of

G

. Show that the two largest ones among the three numbers

d(x,y) + d(z,w), \quad d(x,z) + d(y,w) \quad \text{and} \quad d(x,w) + d(y,z)

are equal.