L. W. Beineke, The decomposition of complete graphs into planar subgraphs. In F. Harary, ed., Graph Theory and Theoretical Physics, pp. 139-154, Academic Press, London, 1967. Home/Search Document Not in Database Summary Related Articles Check |
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Geometric Thickness in a Grid - Wood (2001) (Correct)
....lower and upper bounds for the geometric thickness of complete and complete bipartite graphs. It is shown that d n 1 5:646 e (Kn ) d 4 e. Note that their construction has O(n ) area under the vertex resolution rule [D. Eppstein, personal communication] Since (Kn ) 6 O(1) [3, 4, 6, 21], Kn ) Kn ) for large enough n. On the other hand, K a;b ) K a;b ) when a b [11] Another parameter closely related to geometric thickness is that of book thickness, introduced by Bernhart and Kainen [7] A book consists of a line in 3 space, called the spine, and some number of ....
L. W. Beineke, The decomposition of complete graphs into planar subgraphs. In F. Harary, ed., Graph Theory and Theoretical Physics, pp. 139-154, Academic Press, 1967.
The Thickness of Graphs: A Survey - Mutzel, Odenthal, Scharbrodt (1998) (3 citations) (Correct)
....3.1 is already the exact value. We start with the complete graphs. Theorem 3.2 [AG76] The thickness of the complete graph K n is (K n ) n 7 6 ; for n 6= 9; 10 and (K 9 ) K 10 ) 3: As a by product, the proof of Theorem 3.2 yields the following corollary. Corollary 3. 3 [AG76] [Bei67b] The thickness of the n dimensional octahedron K n(2) is (K n(2) 1 3 n : Along with their work on complete graphs, Beineke and Harary have computed the thickness of complete bipartite graphs in most cases. Theorem 3.4 [BHM64] The thickness of the complete bipartite graph K m;n is (K ....
Beineke, L.W., The decomposition of complete graphs into planar subgraphs, in: Graph theory and theoretical physics, Academic Press, New York (1967), 139--153.
Multi-Dimensional Orthogonal Graph Drawing in the General Position .. - Wood (1999) (1 citation) (Correct)
....graphs. ffl Obviously a graph which admits a 2 D zero bend orthogonal drawing must have thickness at most two. Numerous classes of thickness two graphs, including planar graphs [Wis85] have been shown to admit 2 D zero bend orthogonal drawings [BDHS97] ffl Since K 9 has thickness three (see [Bei67] the 2 D zero bend orthogonal drawing of K 8 in [DH97] is the largest complete graph admitting such a drawing. ffl For D 2 and n 1, K 2D;n has a D dimensional zero bend orthogonal drawing. The construction is the obvious generalization of the result for D = 2 [BDHS97] 37 ffl K 5;6 has a ....
L. W. Beineke. The decomposition of complete graphs into planar subgraphs. In F. Harary, editor, Graph Theory and Theoretical Physics, pages 139--154. Academic Press, London, 1967.
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 ....
L. W. Beineke. The decomposition of complete graphs into planar subgraphs. In F. Harary, editor, Graph Theory and Theoretical Physics, chapter 4, pages 139--153. Academic Press, London, UK, 1967.
Three-Dimensional Orthogonal Graph Drawing - Wood (2000) (3 citations) (Correct)
No context found.
L. W. Beineke, The decomposition of complete graphs into planar subgraphs. In F. Harary, ed., Graph Theory and Theoretical Physics, pp. 139-154, Academic Press, London, 1967.
Three-Dimensional Orthogonal Graph Drawing - Wood (2000) (3 citations) (Correct)
No context found.
L. W. Beineke, The decomposition of complete graphs into planar subgraphs. In F. Harary, ed., Graph Theory and Theoretical Physics, pp. 139-154, Academic Press, London, 1967.
Three-Dimensional Orthogonal Graph Drawing - Wood (2000) (3 citations) (Correct)
No context found.
L. W. Beineke, The decomposition of complete graphs into planar subgraphs. In F. Harary, ed., Graph Theory and Theoretical Physics, pp. 139-154, Academic Press, London, 1967.
Three-Dimensional Orthogonal Graph Drawing - Wood (2000) (3 citations) (Correct)
No context found.
L. W. Beineke, The decomposition of complete graphs into planar subgraphs. In F. Harary, ed., Graph Theory and Theoretical Physics, pp. 139-154, Academic Press, London, 1967.
Remarks On The Thickness Of A Graph - Aho, Mäkinen, Systä (1996) (1 citation) (Correct)
No context found.
L.W. Beineke, The decomposition of complete graphs into planar subgraphs. In: F. Harary (ed.), Graph Theory and Theoretical Physics, Academic Press, London, 1967, 139-154.
Remarks On The Thickness Of A Graph - Aho, Mäkinen, Systä (1996) (1 citation) (Correct)
No context found.
L.W. Beineke, The decomposition of complete graphs into planar subgraphs. In: F. Harary (ed.), ####################################, Academic Press, London, 1967, 139-154.
Geometric Thickness of Complete Graphs - Dillencourt, Eppstein, Hirschberg (2000) (8 citations) (Correct)
No context found.
L. W. Beineke. The decomposition of complete graphs into planar subgraphs. In F. Harary, editor, Graph Theory and Theoretical Physics, chapter 4, pages 139--153. Academic Press, London, UK, 1967.
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