J. Mayer. Decomposition de K 16 en trois graphes planaires. Journal of Combinatorial Theory Series B, 13:71, 1972. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Thickness of Graphs: A Survey - Mutzel, Odenthal, Scharbrodt (1998) (3 citations) (Correct)
....correcting the picture of mathematicians as people in the ivory tower ) Harary made a public offer of 10 to anyone who could compute the thickness of K 16 . It lasted until 1972, when Jean Mayer, surprisingly a professor of french literature ( won the prize by proving that (K 16 ) 3 ([May72]) We now list all known formulas describing the thickness of several graph classes. It is interesting to note that in the case of complete, complete bipartite graphs and hypercubes the lower bound of Theorem 3.1 is already the exact value. We start with the complete graphs. Theorem 3.2 [AG76] ....
Mayer, J., D'ecomposition de K 16 en Trois Graphes Planaires, J. Comb. Theo. (B) 13 (1972), 71.
PQ-trees and maximal planarization - An approach to skewness - Vollen (1998) (Correct)
.... n 7 6 (2.3) It was believed that (2.3) in most cases was an equality. The case was rst settled by Beineke and Harary in 1965 for all n #= 4 (mod 6) Accurate results were found for several values of n = 4 (mod 6) over the next years, the last case of n = 16 was settled in 1972 by Mayer [May72]. This gives the equation (2.4) for the thickness of the complete graph. #(K n ) n 7 6 , n #= 9, 10 and #(K 9 ) #(K 10 ) 3 (2.4) For a more complete historical review and further references, see e.g. Har69] or [Tho95] 2.2.3 Crossing number For G non planar, if embedded in ....
J. Mayer. D#composition de K 16 en trois graphes planaires. J. Combin. Theory B, 13:71, 1972.
Geometric Thickness of Complete Graphs - Dillencourt, Eppstein, Hirschberg (1999) (8 citations) (Correct)
....be reassigned arbitrarily in the plane without altering the topology of the planar embedding provided we are allowed to bend the edges at will [10] This observation is easily verified by induction, moving one vertex at a time. The (graph theoretical) thickness is now known for all complete graphs [1, 2, 3, 12, 13], and is given by the following formula: Kn ) 8 : 1; 1 n 4 2; 5 n 8 3; 9 n 10 Sigma n 2 6 Upsilon ; n 10 (1:1) Another notion related to geometric thickness is the book thickness of a graph G, bt(G) defined as follows [4] A book with k pages or a k book , is a ....
J. Mayer. Decomposition de K16 en trois graphes planaires. Journal of Combinatorial Theory Series B, 13:71, 1972.
Geometric Thickness of Complete Graphs - Dillencourt, Eppstein, Hirschberg (2000) (8 citations) (Correct)
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J. Mayer. Decomposition de K 16 en trois graphes planaires. Journal of Combinatorial Theory Series B, 13:71, 1972.
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