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graphs that can be embedded into the plane, i.e. that can be drawn without crossings between the lines representing edges.

37 votes
2 answers
2k views

A conjecture on planar graphs

I don't know the following is a known result, but it would be very useful to me in my research if it were true. Conjecture: Let $G$ be a planar graph. The sum $$ \sum_{\{x,y\} \in E(G)}{\min(\deg(x),\ …
Zur Luria's user avatar
  • 1,633
8 votes
1 answer
501 views

In how many ways can a given planar graph be mapped into the plane?

I feel sure that this question must have been addressed in the literature, but I can't seem to find it - I may be looking in the wrong place. A graph is planar if it can be drawn on the plane such th …
Zur Luria's user avatar
  • 1,633