  We obtain the following results about the avoidance of ternary formulas. Up
to renaming of the letters, the only infinite ternary words avoiding the
formula $ABCAB.ABCBA.ACB.BAC$ (resp. $ABCA.BCAB.BCB.CBA$) have the same set of
recurrent factors as the fixed point of $\texttt{0}\mapsto\texttt{012}$,
$\texttt{1}\mapsto\texttt{02}$, $\texttt{2}\mapsto\texttt{1}$. The formula
$ABAC.BACA.ABCA$ is avoided by polynomially many binary words and there exist
arbitrarily many infinite binary words with different sets of recurrent factors
that avoid it. If every variable of a ternary formula appears at least twice in
the same fragment, then the formula is $3$-avoidable. The pattern $ABACADABCA$
is unavoidable for the class of $C_4$-minor-free graphs with maximum
degree~$3$. This disproves a conjecture of Grytczuk. The formula $ABCA.ACBA$,
or equivalently the palindromic pattern $ABCADACBA$, has avoidability index
$4$.
