Drawing in three dimensions with one bend per edge.
Devillers, Olivier, Everett, Hazel, Lazard, Sylvain, Pentcheva, Maria, Wismath, Stephen (2006)
Journal of Graph Algorithms and Applications
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Devillers, Olivier, Everett, Hazel, Lazard, Sylvain, Pentcheva, Maria, Wismath, Stephen (2006)
Journal of Graph Algorithms and Applications
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Papakostas, Achilleas, Tollis, Ioannis G. (1999)
Journal of Graph Algorithms and Applications
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Closson, M., Gartshore, S., Johansen, J., Wismath, S.K. (2001)
Journal of Graph Algorithms and Applications
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Di Battista, Giuseppe, Patrignani, Maurizio (2000)
Journal of Graph Algorithms and Applications
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Biedl, T., Shermer, T., Whitesides, S., Wismath, S. (1999)
Journal of Graph Algorithms and Applications
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Di Giacomo, Emilio, Didimo, Walter, Liotta, Giuseppe, Meijer, Henk (2005)
Journal of Graph Algorithms and Applications
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Cornelsen, Sabine, Schank, Thomas, Wagner, Dorothea (2004)
Journal of Graph Algorithms and Applications
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Angelini, Patrizio, Cittadini, Luca, Didimo, Walter, Frati, Fabrizio, Di Battista, Giuseppe, Kaufmann, Michael, Symvonis, Antonios (2011)
Journal of Graph Algorithms and Applications
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Valerii A. Aksenov, Oleg V. Borodin, Anna O. Ivanova (2016)
Discussiones Mathematicae Graph Theory
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In 1955, Kotzig proved that every 3-connected planar graph has an edge with the degree sum of its end vertices at most 13, which is tight. An edge uv is of type (i, j) if d(u) ≤ i and d(v) ≤ j. Borodin (1991) proved that every normal plane map contains an edge of one of the types (3, 10), (4, 7), or (5, 6), which is tight. Cole, Kowalik, and Škrekovski (2007) deduced from this result by Borodin that Kotzig’s bound of 13 is valid for all planar graphs with minimum degree δ at least 2...
Biedl, Therese C. (1998)
Journal of Graph Algorithms and Applications
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Wood, David R. (2003)
Journal of Graph Algorithms and Applications
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Oleg V. Borodin, Anna O. Ivanova, Tommy R. Jensen (2014)
Discussiones Mathematicae Graph Theory
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It is known that there are normal plane maps M5 with minimum degree 5 such that the minimum degree-sum w(S5) of 5-stars at 5-vertices is arbitrarily large. In 1940, Lebesgue showed that if an M5 has no 4-stars of cyclic type (5, 6, 6, 5) centered at 5-vertices, then w(S5) ≤ 68. We improve this bound of 68 to 55 and give a construction of a (5, 6, 6, 5)-free M5 with w(S5) = 48
Di Giacomo, Emilio, Didimo, Walter, Liotta, Giuseppe, Palladino, Pietro (2010)
Journal of Graph Algorithms and Applications
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