 Boolean literal

A Boolean literal is a Boolean variable $u$ or its logical negation $\neg u$. The two Boolean literals have opposite truth values: a Boolean valuation $v$ gives $v(\neg u)=1-v(u)$ when false and true are encoded as zero and one. Thus $u=0$ makes the positive Boolean literal $u$ false and the negative Boolean literal $\neg u$ true. A Boolean clause combines Boolean literals, and a Boolean-pair colouring gadget represents a Boolean variable and its logical negation by two vertices with opposite Boolean colours.