There wasn't a separate forum for this subject so i posted it here with hopes of someone being able to help me out. I am currently working on a problem set and i am working on looking at graphs and identifying if they are planar or not. I read through the chapter and no where did it state specifics on certain topics. I have posted the few questions that I have below. Thanks again for your help and time and sorry if this was posted under the wrong section.

-In identifying a planar graph does it have to have a hamilton circuit?
-How can i identify a k3,3 graph. I understand that K3,3 graphs are bipartite and have 6 vertices with degree of 3 per vertices but i have a graph where the answer states it has many k3,3 graphs. How do i go about identifying these? and while on the topic can you shed light on a k5 graph as well? Thanks again.