How to show that the following graph is planar?
I tried to redraw the graph but I cant draw it without the edges crossing.
Also I find that the edges $3,4,5$ form a complete graph.
Also I am unable to find any subdivision of $K_5$ or $K_{3,3}$.
So I am confused whether it is planar or not?
Best Answer
Place vertices $5$ and $1$ inside triangle $234$. Graph with $5$ vertices can't be subdivision of $K_{3,3}$, and it can be subdivision of $K_5$ only if it's $K_5$ itself.