Bull. Korean Math. Soc. 2022; 59(1): 27-43
Online first article January 31, 2022 Printed January 31, 2022
https://doi.org/10.4134/BKMS.b201080
Copyright © The Korean Mathematical Society.
Jaeyoo Choy, Hahng-Yun Chu
Chungnam National University; Chungnam National University
The one-sided fattenings (called semi-ribbon graph in this paper) of the graph embedded in the real projective plane $\mathbb R\mathbb P^{2}$ 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 $\mathbb R\mathbb P^{2}$ 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
Supported by: 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.
2024; 61(2): 557-584
2022; 59(3): 745-756
2019; 56(1): 73-82
2018; 55(2): 415-430
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd