Bulletin of the
Korean Mathematical Society BKMS

The one-sided fattenings (called semi-ribbon graph in this paper) of the graph embedded in the real projective plane $\rrpp^{2}$ are completely classified up to topological equivalence. A planar graph (i.e., embedded in the plane), admitting the one-sided fattening, is known to be a cactus boundary. For the graphs embedded in $\rrpp^{2}$ admitting the one-sided fattening, unlike the planar graphs, a new building block appears: a bracelet along the M\"obius band, which is not a connected summand of the oriented surfaces.

Keywords: Fattening, one-sided fattening, graph, ribbon graph, semi-ribbon graph, pre-semi-ribbon graph, Riemann surface, real projective plane, planar graph

MSC numbers: Primary 05C10, 05C38, 37C10