Geodesic
A note on the upper bounds on the size of bipartite and tripartite 1-embeddable graphs on surfaces
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 1, pp. 171-177

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In this note, we show sharp upper bounds of the size of simple bipartite and tripartite 1-embeddable graphs on closed surfaces.
Keywords: $1$-embedding, bipartite graph, tripartite graph 
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Shibuya, Hikari; Suzuki, Yusuke. A note on the upper bounds on the size of bipartite and tripartite 1-embeddable graphs on surfaces. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 1, pp. 171-177. http://geodesic.mathdoc.fr/item/DMGT_2023_43_1_a10/