A problem has come up in which I have a partial order $\leq$ and I need to extend it to a linear order $\leq^{*}$ obeying a series of restrictions that, for given elements $a,b,c$, $a \leq^{*} b \leq^{*} c$ is forbidden. $a \leq^{*} b$, $a \leq^{*} c$ and $b \leq^{*} c$ are all allowed: the restriction only forbids that $b$ is placed in between $a$ and $c$. In summary, if $a \leq^{*} c$, then either $b \leq^{*} a$ or $c \leq^{*} b$.
Does this type of linear extension have a name?