Math question

Pls see attached

Math question

pls see attached

Spanning Trees and Graphs

Does every graph have a spanning tree? If not, then can you tell from the number of nodes and the number of edges a graph has whether it has a spanning tree, or do you need more information?

Spanning Tree Graph

If you were required by a professor to find a spanning tree of the movie collaboration graph (where each node corresponds to an actor with finite Kevin Bacon number, and two nodes are connected by an edge if the corresponding actors have been in a movie together), how would you do it? Why would you choose your method over other possible methods?

Tile a plane with n-gons

Is it possible to tile a plane with (a) regular 5-gons and regular 6-gons? (B) regular 5-gons, regular 6-gons, and triangles? (c) regular 5-gons, regular 6-gons, and regular triangles?