Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ONE-SIDED FATTENING OF THE GRAPH IN THE REAL PROJECTIVE PLANE

  • Choy, Jaeyoo (Department of Mathematics Chungnam National University) ;
  • Chu, Hahng-Yun (Department of Mathematics Chungnam National University)
  • Received : 2020.12.29
  • Accepted : 2021.09.09
  • Published : 2022.01.31
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Abstract

The one-sided fattenings (called semi-ribbon graph in this paper) of the graph embedded in the real projective plane ℝℙ2 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 ℝℙ2 admitting the one-sided fattening, unlike the planar graphs, a new building block appears: a bracelet along the Möbius band, which is not a connected summand of the oriented surfaces.

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Acknowledgement

The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1C1C2011737). The second author was supported by research fund of Chungnam National University.

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