Geodesic
The structure of neighborhoods of 5-vertices in normal plane maps with minimum degree 5
Matematičeskie zametki SVFU, Tome 23 (2016) no. 1, pp. 56-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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In 1940, Lebesgue described the neighborhoods of vertices of degree 5 in normal plane maps with minimum degree 5 (M5), presenting only an idea of the proof but not the details. The paper presents a detailed scheme of a complete proof of Lebesgue's description with improving two of its parameters without worsening the others. Moreover, it is present a scheme of the proof of the height of a 5-star (the maximum degree of its vertices) in an M5, which improves the result of O.V.Borodin, A.O.Ivanova, T.R.Yensen (2013).
Keywords: plane graph, normal plane maps, neighborhood.
Mots-clés : structure 
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D. V. Nikiforov. The structure of neighborhoods of 5-vertices in normal plane maps with minimum degree 5. Matematičeskie zametki SVFU, Tome 23 (2016) no. 1, pp. 56-66. http://geodesic.mathdoc.fr/item/SVFU_2016_23_1_a5/

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