### Table 1: Volume of 3D polyline drawings of n-vertex graphs with m n edges.

2004

"... In PAGE 2: ... Only recently have (non-orthogonal) polyline drawings been considered [11, 13]. Table1 summarises the best known upper bounds on the volume and bends per edge in polyline drawings. Cohen et al.... In PAGE 3: ... Every complete graph Kn, and hence every n-vertex graph, has a 1-bend O(log n) O(n) O(n2= log3 n) drawing with O(n3= log2 n) volume. It is not straightforward to compare the volume bound in Theorem 2 with the O(kqm) bound by Dujmovi c and Wood [11] for k-colourable q-queue graphs (see Table1 ). However, since k 4q and m 2qn (see [10]), we have that O(kqm) O(q3n), and thus the O(kqm) bound by Dujmovi c and Wood [11] is no more than the bound in Theorem 2 whenever the graph has a O((n= log n)2=3)-queue layout.... ..."

Cited by 4

### Table 2: Best known bounds on the maximum number of edges in an n-vertex graph with a given girth.

2001

"... In PAGE 20: ... More on this can be found in [TZ01]. Acknowledgment We would like to thank Edith Cohen for her results that inspired this research and for making the coop- eration between the authors possible, Felix Lazebnik for his help in compiling Table2 , and Michael Elkin for pointing out the connection between distance oracles and distance labels. References [ABCP99] B.... ..."

Cited by 108

### Table 1. Collective additive tree spanners of n-vertex graphs having balanced separa- tors of bounded size

"... In PAGE 7: ... Every graph with tree-width at most k is (1/2,k+1, 0)-decomposable. Table1 summarizes the results on collective additive tree spanners of graphs having balanced separators of bounded size. The results are obtained by com-... ..."

### TABLE II. BEST KNOWN BOUNDS ON THE MAXIMUM NUMBER OF EDGES IN AN n-VERTEX GRAPH WITH A GIVEN GIRTH

### Table 1. Upper bounds on the volume of 3D drawings of n-vertex m-edge graphs.

2004

Cited by 17

### Table 1. Bounds on the volume, aspect ratio, and bit-requirement of various kinds of crossing-free 3D drawings of an N-vertex graph.

"... In PAGE 2: ... Small volume, small aspect ratio, large angular resolution, large edge-separation, and small bit-requirement are generally desirable for a drawing [11, 12]. Table1 summarizes some known results on the volume-requirement, aspect ratio, and bit-requirement of various kinds of crossing-free 3D drawings. Research on 3D drawings of graphs has mainly concentrated on two types of drawings: straight line drawings and orthogonal grid drawings.... ..."

### Table 1 and by Lemma 3.1 this shows that for an n-vertex cubic graph, algorithm Edge Greedy returns an I-EDS of size at most 9n=20 + O(1).

### Table 1 Complexity Analysis of various phases of our parallel solver for N-vertex constant node-degree graphs.

"... In PAGE 6: ... Refer to [3] for details. 5 Analysis and Preliminary Experimental Results Table1 shows the serial and parallel time complexities of the various phases of our parallel direct solver for matrices corresponding to 2-D and 3-D nite element meshes [2, 1, 3]. From this table we see that the overall time complexity is dominated by the numerical factorization phase.... ..."

### Table 1 Complexity Analysis of various phases of our parallel solver for N-vertex constant node-degree graphs.

"... In PAGE 6: ... Refer to [3] for details. 5 Analysis and Preliminary Experimental Results Table1 shows the serial and parallel time complexities of the various phases of our parallel direct solver for matrices corresponding to 2-D and 3-D nite element meshes [2, 1, 3]. From this table we see that the overall time complexity is dominated by the numerical factorization phase.... ..."

### Table 4: Clique-size performance and running time of MFA-CM on N-vertex p-random graphs, averaged over R graphs in each row. N=R p

1996

"... In PAGE 7: ... We chose 100-vertex 0.9-random graphs both so as to evaluate many more parameter settings and also to test if the best parameter settings would later scale up to larger graphs (see Table4 ). Table 3 reports our experiments.... In PAGE 8: ... We then tested if the parameter setting P1(N) would scale up to larger graphs and the running time of MFA-CM with this parameter setting on these graphs. Table4 reports the results. The rows with the same values of N and p were tested on identical graphs.... In PAGE 8: ... (In earlier experiments [JR92] on the same ten 400-vertex 0.9-random graphs as in Table4 , we obtained an average clique size of 50.4 with a slow geometric annealing schedule and an average clique size of 43.... ..."

Cited by 15