Guichard-Combinatorics-Graph-Theory · Problem 5.4.1

Graph Theory

Mathematics — Probability · bipartite-graphs

Problem

Prove that there is a bipartite multigraph with degree sequence

d_1, \ldots, d_n

if and only if there is a partition

\{I, J\}

[n]

such that

\sum_{i \in I} d_i = \sum_{i \in J} d_i.