Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2022; 59(1): 27-43

Published online January 31, 2022 https://doi.org/10.4134/BKMS.b201080

Copyright © The Korean Mathematical Society.

One-sided fattening of the graph in the real projective plane

Jaeyoo Choy, Hahng-Yun Chu

Chungnam National University; Chungnam National University

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.

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.