Combinatorics and Graph Theory · Problem 5.5.6

Graph Theory — David Guichard

Mathematics — Combinatorics · trees

Problem

Let

n \geq 2

. Show that there is a tree with degree sequence

d_1, d_2, \ldots, d_n

if and only if

d_i > 0

for all

i

and

\sum_{i=1}^n d_i = 2(n-1)