diff --git a/src/graph/2SAT.md b/src/graph/2SAT.md index b66316bbe..c9dd6f4a5 100644 --- a/src/graph/2SAT.md +++ b/src/graph/2SAT.md @@ -39,7 +39,10 @@ b \Rightarrow a & \lnot b \Rightarrow \lnot a & b \Rightarrow \lnot a & c \Right You can see the implication graph in the following image: -
!["Implication Graph of 2-SAT example"](2SAT.png)
+

+ Implication Graph of 2-SAT example +

+ It is worth paying attention to the property of the implication graph: if there is an edge $a \Rightarrow b$, then there also is an edge $\lnot b \Rightarrow \lnot a$. @@ -59,7 +62,9 @@ The following image shows all strongly connected components for the example. As we can check easily, neither of the four components contain a vertex $x$ and its negation $\lnot x$, therefore the example has a solution. We will learn in the next paragraphs how to compute a valid assignment, but just for demonstration purposes the solution $a = \text{false}$, $b = \text{false}$, $c = \text{false}$ is given. -
!["Strongly Connected Components of the 2-SAT example"](2SAT_SCC.png)
+

+ Strongly Connected Components of the 2-SAT example +

Now we construct the algorithm for finding the solution of the 2-SAT problem on the assumption that the solution exists.