  In Ramsey theory for graphs we are given a graph $G$ and we are required to
find the least $n_0$ such that, for any $n\geq n_0$, any red/blue colouring of
the edges of $K_n$ gives a subgraph $G$ all of whose edges are blue or all are
red. Here we shall be requiring that, for any red/blue colouring of the edges
of $K_n$, there must be a copy of $G$ such that its edges are partitioned
equally as red or blue (or the sizes of the colour classes differs by one in
the case when $G$ has an odd number of edges). This introduces the notion of
balanceable graphs and the balance number of $G$ which, if it exists, is the
minimum integer bal$(n, G)$ such that, for any red/blue colouring of $E(K_n)$
with more than bal$(n, G)$ edges of either colour, $K_n$ will contain a
balanced coloured copy of $G$ as described above.
  This parameter was introduced by Caro, Hansberg and Montejano in
\cite{2018arXivCHM}. There, the authors also introduce the strong balance
number sbal$(n,G)$ and the more general omnitonal number ot$(n, G)$ which
requires copies of $G$ containing a complete distribution of the number of red
and blue edges over $E(G)$.
  In this paper we shall catalogue bal$(n, G)$, sbal$(n, G)$ and ot$(n,G)$ for
all graphs $G$ on at most four edges. We shall be using some of the key results
of Caro et al, which we here reproduce in full, as well as some new results
which we prove here. For example, we shall prove that the union of two
bipartite graphs with the same number of edges is always balanceable.
