Question

Advanced Physics
Show that every trivalent map on the sphere has a face with fewer than six sides​

Answer 1

$\huge \mathbb\fcolorbox{black}{mediumpurple}{Answer♡}$

It is enough to show that any trivalent map on S2 can be 5-colored. Lemma. Any trivalent map on the sphere has a face with fewer than six sides. Proof.

Answer 2

$\huge \mathbb\fcolorbox{black}{mediumpurple}{Answer♡}$

It is enough to show that any trivalent map on S2 can be 5-colored. Lemma. Any trivalent map on the sphere has a face with fewer than six sides. Proof.