Labeling angles of planar graphs (Q1115878)

By a well-known theorem of Heawood, 3-edge-coloring bridgeless planar cubic graphs is equivalent to labeling vertices with \(+1\) or -1 so that the sum around any face is 0(mod 3). The authors introduce the notion of ``angle-labeling'' and prove results analogous to Heawood's for bridgeless planar graphs with vertices of degree 2 or 3; the angles and edge-sides are labeled by elements of the group \(S_ 3\).