MathDB

Given two positive integers

m

and

n

, find the largest

k

in terms of

m

and

n

such that the following condition holds:
Any tree graph

G

with

k

vertices has two (possibly equal) vertices

u

and

v

such that for any other vertex

w

G

, either there is a path of length at most

m

from

u

w

, or there is a path of length at most

n

from

v

w

.
Proposed by Ivan Chan Kai Chin

8