One-sided fattening of the graph in the real projective plane
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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.
Abstract
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.
참고문헌 (11)
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