### Table 3: Lower bounds for the average number of bends per edge.

"... In PAGE 26: ... BulletBulletBullet BulletBulletBullet BulletBulletBullet BulletBulletBullet BulletBulletBullet BulletBulletBullet BulletBulletBullet BulletBulletBullet BulletBulletBullet BK BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BO BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BM D6 D8CXD1CTD7 Figure 29: 6-connected 6-regular graphs (Cr C3 C3)hK6i and (Cr C3 C3)hK7 n M3i. In Table3 we prove lower bounds on the number of bends in drawings of the above families of graphs. Each line of the table corresponds to one such family HhGi (or H G) parameterised by some value r, all of which have maximum degree (shown in the rst column).... In PAGE 28: ...60 Table3 : continued HhGi or H G #bends(G) #copies(G) #edges avg. #bends 2-Connected Pseudographs 6 CrhL2i 6 r 3r 2 ? 4 CrhL1i 3 r 2r 3 2 ? 3-Connected Simple Graphs 6(Cr K2)hK6i 12 (Thm.... In PAGE 29: ...61 Table3 : continued HhGi or H G #bends(G) #copies(G) #edges avg. #bends 5-Connected Simple Graphs 6(Cr C3 K2)hK6i 12 (Thm.... ..."

Cited by 5

### Table 3: Lower bounds for the average number of bends per edge.

2000

"... In PAGE 26: ... Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet Bullet BK BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BO BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BQ BM D6 times Figure 29: 6-connected 6-regular graphs B4BVD6 A2 BVBF A2 BVBFB5CWC3BICX and B4BVD6 A2 BVBF A2 BVBFB5CWC3BJ D2 C5BFCX. In Table3 we prove lower bounds on the number of bends in drawings of the above families of graphs. Each line of the table corresponds to one such family C0CWBZCX (or C0 A2 BZ) parameterised by some value D6, all of which have max- imum degree A1 (shown in the first column).... In PAGE 28: ... Table3 : continued A1 C0CWBZCX or C0 A2 BZ #bends(BZ) AL #copies(BZ) #edges avg. #bends AL 2-Connected Pseudographs BI BVD6CWC4BECX BI D6 BFD6 BE BR BG BVD6CWC4BDCX BF D6 BED6 BF BE BR 3-Connected Simple Graphs 6 B4BVD6 A2 C3BEB5CWC3BICX 12 (Theorem 7) BED6 BFBFD6 BEA1BDBE BFBF BP BK BDBD BR 6 B4BVD6 A2 C3BEB5CWC3BJ D2 C5BECX 14 (Theorem 9) BED6 BGBDD6 BEA1BDBG BGBD BP BEBK BGBD 5 B4BVD6 A2 C3BEB5CWC3BHCX 7 (Theorem 4) BED6 BEBFD6 BEA1BJ BEBF BP BDBGBEBF BR 5 B4BVD6 A2 C3BEB5CWC3BI D2 C5BECX 8 (Theorem 7) BED6 BEBLD6 BEA1BK BEBL BP BDBIBEBL 4 B4BVD6 A2 C3BEB5CWC3BGCX 3 (Theorem 2) BED6 BDBHD6 BEA1BF BDBH BP BEBH 4 B4BVD6 A2 C3BEB5CWC3BH D2 C5BECX 4 (Theorem 5) BED6 BDBLD6 BEA1BG BDBL BP BK BDBL BR 3 B4BVD6 A2 C3BEB5CWC3BFCX 1 (Observation 3) BED6 BLD6 BEBL BR 3-Connected Multigraphs 6 BVD6 A2 B4BG A1 C3BEB5 6 (Lemma 7) D6 BID6 BI BI BP BD BR 5 BVD6 A2 B4BF A1 C3BEB5 4 (Lemma 7) D6 BHD6 BG BH BR 4 BVD6 A2 B4BE A1 C3BEB5 2 (Lemma 7) D6 BGD6 BE BG BP BDBE BR 3-Connected Pseudographs BI BVD6 A2 B4B4BE A1 C3BEB5CWC4BDCXB5 BK D6 BID6 BG BF BR BH B4BVD6 A2 C3BEB5CWC4BDCX BF BED6 BHD6 BI BH BR 4-Connected Simple Graphs 6 B4BVD6 A2 BVBFB5CWC3BICX 12 (Theorem 7) BFD6 B4BF A1 BDBH B7 BIB5D6 BFA1BDBE BHBD BP BDBE BDBJ BR 6 B4BVD6 A2 BVBFB5CWC3BJ D2 C5BECX 14 (Theorem 9) BFD6 B4BF A1 BDBL B7 BIB5D6 BFA1BDBG BIBF BP BE BF 5 B4BVD6 A2 BVBFB5CWC3BHCX 7 (Theorem 4) BFD6 B4BF A1 BDBC B7 BIB5D6 BFA1BJ BFBI BP BJ BDBE BR 5 B4BVD6 A2 BVBFB5CWC3BI D2 C5BECX 8 (Theorem 7) BFD6 B4BF A1 BDBF B7 BIB5D6 BFA1BK BGBH BP BK BDBH 4 B4BVD6 A2 BVBFB5CWC3BGCX 3 (Theorem 2) BFD6 B4BF A1 BI B7 BIB5D6 BFA1BF BEBG BP BFBK 4 B4BVD6 A2 BVBFB5CWC3BH D2 C5BECX 4 (Theorem 5) BFD6 B4BF A1 BK B7 BIB5D6 BFA1BG BFBC BP BEBH BR 4-Connected Multigraphs 5 BVD6 A2 B4BFBE A1 BVBGB5 BG (Lemma 7) D6 BDBCD6 BG BDBC BP BEBH BR 6 BVD6 A2 B4BE A1 BVBFB5 BI (Lemma 7) D6 BLD6 BI BL BP BEBF BR 4-Connected Pseudographs BI B4BVD6 A2 BVBFB5CWC4BDCX BF BFD6 B4BF A1 BD B7 BIB5D6 BL BL BP BD BR... In PAGE 29: ... Table3 : continued A1 C0CWBZCX or C0 A2 BZ #bends(BZ) AL #copies(BZ) #edges avg. #bends AL 5-Connected Simple Graphs 6 B4BVD6 A2 BVBF A2 C3BEB5CWC3BICX 12 (Theorem 7) BID6 B4BI A1 BDBH B7 BDBHB5D6 BIA1BDBE BDBCBH BP BEBG BFBH BR 6 B4BVD6 A2 BVBF A2 C3BEB5CWC3BJ D2 C5BFCX 11 (Theorem 9) BID6 B4BI A1 BDBK B7 BDBHB5D6 BIA1BDBD BDBEBF BP BEBE BGBD 5 B4BVD6 A2 BVBF A2 C3BEB5CWC3BHCX 7 (Theorem 4) BID6 B4BI A1 BDBC B7 BDBHB5D6 BIA1BJ BJBH BP BDBGBEBH BR 5-Connected Multigraphs 6 BVD6 A2 BVBF A2 B4BE A1 C3BEB5 BE (Lemma 7) BFD6 BDBKD6 BEA1BF BDBK BP BDBF BR 6-Connected Simple Graphs 6 B4BVD6 A2 BVBF A2 BVBFB5CWC3BICX 12 (Theorem 7) BLD6 B4BL A1 BDBH B7 BEBJB5D6 BLA1BDBE BDBIBE BP BE BF BR 6 B4BVD6 A2 BVBF A2 BVBFB5CWC3BJ D2 C5BFCX 11 (Theorem 9) BLD6 B4BL A1 BDBK B7 BEBJB5D6 BLA1BDBD BDBKBL BP BDBD BEBD 5 Lower Bounds for General Position Drawings Recall that a 3-D orthogonal graph drawing is said to be in general position if no two vertices lie in a common grid-plane.... ..."

Cited by 25

### Table 1 suggests a trade-off between the number of bends per edge and the bounding box volume.

"... In PAGE 7: ... We also present refinements of both our algorithms with one less bend per edge, at the cost of an increase in the volume. Table1 summarises the known bounds for orthogonal graph drawing. 2 Lower Bounds In this section we prove lower bounds on the volume of orthogonal graph drawings.... ..."

### Table 3. 6-bend edge route for vw

1999

"... In PAGE 7: ...eight, as illustrated in Fig. 2. Suppose the grid points on v and w assigned to vw are respectively (vX; vY ; 0) and (wX; wY ; 0). The edge vw is routed as in Table3 and illustrated in Fig. 3.... ..."

Cited by 8

### Table 1: Overview of the achieved bounds. In our algorithm the 3-bent edge only occurs for the octahedron. Even amp; Granot [6] proved that this graph indeed requires a 3-bent edge. Hence the octahedron is the only 4-graph which cannot be drawn with at most two bends per edge.

1994

Cited by 61

### Table 2 Comparison of the GIST andGMST on three diVTerent graphs a

"... In PAGE 14: ... A simple example will serve to illustrate this point. Table2 compares the weight andtortuosity of trees generated on several underlying graphs. The FFrst data set is for the graph used in generating Fig.... In PAGE 15: ...rom a Gaussian distribution with mean 0.5. The Gaussian distribution was scaled such that the standard deviation matched that of a uniform distribution between 0 and 1, with values below 0 or above 1 set to the appropriate extreme. The statistical properties of the GIST andGMST on this graph are listedin Table2 as Graph 3. The results are very similar to those for a graph with uniformly distributed edge weights.... ..."

### Table 2: Results from the test graphs; bits per edge.

2001

"... In PAGE 8: ... This data set is larger than our random sets; hence again to construct the affinity graph on the TREC database we only created edges between pages with at least three shared links. Table2 presents the compression results in terms of total bits required divided by edges in the graph. For the random graphs, we have taken the average of ten trials, where a different random graph is produced for each trial.... ..."

Cited by 49

### Table 2: Results from the test graphs; bits per edge.

2001

"... In PAGE 8: ... This data set is larger than our random sets; hence again to construct the affinity graph on the TREC database we only created edges between pages with at least three shared links. Table2 presents the compression results in terms of total bits required divided by edges in the graph. For the random graphs, we have taken the average of ten trials, where a different random graph is produced for each trial.... ..."

Cited by 49

### Table 2: Results from the test graphs; bits per edge.

2001

"... In PAGE 8: ... This data set is larger than our random sets; hence again to construct the affinity graph on the TREC database we only created edges between pages with at least three shared links. Table2 presents the compression results in terms of total bits required divided by edges in the graph. For the random graphs, we have taken the average of ten trials, where a different random graph is produced for each trial.... ..."

Cited by 49

### Table 2: Results from the test graphs; bits per edge.

in Abstract