Bounded-degree graphs have arbitrarily large geometric thickness.
Barát, János, Matoušek, Jirí, Wood, David R. (2006)
The Electronic Journal of Combinatorics [electronic only]
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Barát, János, Matoušek, Jirí, Wood, David R. (2006)
The Electronic Journal of Combinatorics [electronic only]
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Caro, Yair, West, Douglas B. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Bagga, Jay (2004)
International Journal of Mathematics and Mathematical Sciences
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Liebers, Annegret (2001)
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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Xin Zhang, Guizhen Liu (2013)
Open Mathematics
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If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is Δ if Δ ≥ 8, the list edge (resp. list total) chromatic number of G is Δ (resp. Δ + 1) if Δ ≥ 14 and the linear arboricity...
Djidjev, Hristo N., Vrt'o, Imrich (2003)
Journal of Graph Algorithms and Applications
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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.
M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, I. Gutman (2013)
Kragujevac Journal of Mathematics
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Cheston, Grant A., Jap, Tjoen Seng (2006)
Journal of Graph Algorithms and Applications
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