Track layouts of graphs.
Dujmović, Vida, Pór, Attila, Wood, David R. (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Dujmović, Vida, Pór, Attila, Wood, David R. (2004)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Dujmović, Vida, Wood, David R. (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Liebers, Annegret (2001)
Journal of Graph Algorithms and Applications
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Juraj Bosák (1984)
Mathematica Slovaca
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Dickerson, Matthew, Eppstein, David, Goodrich, Michael T., Meng, Jeremy Y. (2005)
Journal of Graph Algorithms and Applications
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Gary Chartrand, Farrokh Saba, Hung Bin Zou (1985)
Časopis pro pěstování matematiky
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Wood, David R. (2006)
The Electronic Journal of Combinatorics [electronic only]
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Carmi, Paz, Dujmovic, Vida, Morin, Pat, Wood, David R. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Xin Zhang, Yong Yu, Guizhen Liu (2011)
Open Mathematics
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A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ(G) ≥ 8p+4 or Δ(G) ≥ 6p+2 and g(G) ≥ 4. As a consequence, the well-known (p, 1)-total labelling conjecture has been confirmed for some 1-planar graphs.