### TABLE 2.1. Splitter theorems and generating theorems for 3-regular k-connected graphs with girth at least g.

2003

### Table 1: Summary of results on methods for k-path and k-connectivity queries.

1999

"... In PAGE 3: ... For general graphs and k 4, or for (k ?1)-connected graphs and xed k gt; 4, there are O(n)-space data structures that perform k-connectivity queries in O(1) time, but do not support output-sensitive k-path queries (see [42, 51] for k = 2, [14] for k = 3, [28] for k = 4, and [9] for k gt; 4). Table1 in Appendix A summarizes previous and new results on methods for k-path and k- connectivity queries. 1.... In PAGE 37: ...Results on k-Path and k-Connectivity Queries Table1 summarizes the previous and new results on methods for k-path and k-connectivity queries.... ..."

Cited by 9

### Table 1: Summary of results on methods for k-path and k-connectivity queries.

"... In PAGE 3: ... For general graphs and k 4, or for (k ? 1)-connected graphs and xed k gt; 4, there are O(n)-space data structures that perform k-connectivity queries in O(1) time, but do not support output-sensitive k-path queries (see [42, 51] for k = 2, [14] for k = 3, [28] for k = 4, and [9] for k gt; 4). Table1 in Appendix A summarizes previous and new results on methods for k-path and k-connectivity queries. 1.... In PAGE 36: ...Results on k-Path and k-Connectivity Queries Table1 summarizes the previous and new results on methods for k-path and k-connectivity... ..."

### Table 1 summarizes the previous and new results on methods for k-path and k-connectivity

"... In PAGE 3: ... For general graphs and k 4, or for (k ; 1)-connected graphs and xed k gt;4, there are O(n)-space data structures that perform k-connectivity queries in O(1) time, but do not support output-sensitive k-path queries (see [42,51]fork = 2, [14]fork =3,[28] for k = 4, and [9] for k gt;4). Table1 in Appendix A summarizes previous and new results on methods for k-path and k-connectivity queries. 1.... In PAGE 36: ... Table1 : Summary of results on methods for k-path and k-connectivity queries. B The SPQR-Tree In this appendix, the SPQR-tree presented in [15, 14] is described.... ..."

### Table 3 and the runtimes are also preferable to GRASP. A comparison of performances for a variety of values of k-connectivity and c-domination is given in Table 5.

"... In PAGE 11: ...5 7 7 7 Mean Excess 0% 17.1% Table3 : Optimality Tests for k=2 4.2 Comparisons between MRP/SA, MRP/Drop and MRP/GRASP In the absence of a known optimum for more complex instances, we look for a relative improvement in CDS size for SA and GRASP over the greedy MRP/Drop.... ..."

### Table 2.1: The number of nodes n required to achieve k-connectivity with probability q when r=pA is as in Figure 2.6, as predicted by our quantile models for R1(N), R2(N), and R3(N)

### Table 1: Connectivity: A 3-regular random graph and a 3-Araneola overlay has a connectivity of 3. The rest of the graphs have a connectivity of 1 or 0.

"... In PAGE 3: ... THE METRICS 4.1 Connectivity Table1 presents the connectivity of the different graphs. A k-regular random graph and a k-Araneola graph are almost always k connected [10, 8].... ..."

### Table 1: Connectivity: A 3-regular random graph and a 3-Araneola overlay has a connectivity of 3. The rest of the graphs have a connectivity of 1 or 0.

"... In PAGE 3: ... THE METRICS 4.1 Connectivity Table1 presents the connectivity of the different graphs. A k-regular random graph and a k-Araneola graph are almost always k connected [10, 8].... ..."

### Table 1. Summary of results. NPCmeans that the problem is NP-complete.

1997

"... In PAGE 3: ... Since we can prove that it is NP-complete to decide whether a 2-connected planar graph of maximum degree 2 T ? 1 has a T -spanning tree, this result establishes a complete characterization of the T -spanning tree problem for k-connected planar graphs of maximum degree G. Table1 summarizes the results (it assumes that G gt; T 2). Organization of the paper Section 2 provides basic terminology.... ..."

Cited by 5

### Table 1. Summary of results. NPCmeans that the problem is NP-complete.

1997

"... In PAGE 3: ... Since we can prove that it is NP-complete to decide whether a 2-connected planar graph of maximum degree 2 T ? 1 has a T -spanning tree, this result establishes a complete characterization of the T -spanning tree problem for k-connected planar graphs of maximum degree G. Table1 summarizes the results (it assumes that G gt; T 2). Organization of the paper Section 2 provides basic terminology.... ..."

Cited by 5