### Table 1. Number of crossings of spanning trees in airline graphs.

2005

Cited by 2

### Table 1 summarizes the characterization results about the -drawability of outerplanar graphs. The entries having a bibliographic reference describe previously known results. All other entries describe results from this paper. fCOg, fBOg, and fMOg are the set of all connected outerplanar, biconnected outerplanar, and maximal outerplanar graphs, respectively. GCO( ), GBO( ), and GMO( ) are the classes of connected outerplanar, bicon- nected outerplanar, and maximal outerplanar ( )-drawable graphs, respectively. Similarly, GCO[ ], GBO[ ], and GMO[ ] are the classes of connected outerplanar, biconnected outerplanar, and maximal outerplanar [ ]-drawable graphs, respectively. Gk denotes the class of graphs such that the number of biconnected components sharing a cut-vertex is at most k; Tk is the class of trees whose vertex degree is at most k; T is the class of forbidden trees described in [3].

"... In PAGE 5: ... Table1 : Summarizing the characterization results on the -drawability of outerplanar graphs for 1 2. 2 Preliminaries We review rst standard de nitions on outerplanar graphs.... ..."

### Table 1 summarizes the characterization results about the -drawability of outerplanar graphs. The entries having a bibliographic reference describe previously known results. All other entries describe results from this paper. fCOg, fBOg, and fMOg are the set of all connected outerplanar, biconnected outerplanar, and maximal outerplanar graphs, respectively. GCO( ), GBO( ), and GMO( ) are the classes of connected outerplanar, bicon- nected outerplanar, and maximal outerplanar ( )-drawable graphs, respectively. Similarly, GCO[ ], GBO[ ], and GMO[ ] are the classes of connected outerplanar, biconnected outerplanar, and maximal outerplanar [ ]-drawable graphs, respectively. Gk denotes the class of graphs such that the number of biconnected components sharing a cut-vertex is at most k; Tk is the class of trees whose vertex degree is at most k; T is the class of forbidden trees described in [3].

"... In PAGE 4: ... Table1 : Summarizing the characterization results on the -drawability of outerplanar graphs for 1 2. 2 Preliminaries We review rst standard de nitions on outerplanar graphs.... ..."

### Table 1 summarizes the characterization results about the -drawability of outerplanar graphs. The entries having a bibliographic reference describe previously known results. All other entries describe results from this paper. fCOg, fBOg, and fMOg are the sets of all connected outerplanar, biconnected outerplanar, and maximal outerplanar graphs, respectively. GCO( ), GBO( ), and GMO( ) are the classes of connected outerplanar, bicon- nected outerplanar, and maximal outerplanar ( )-drawable graphs, respectively. Similarly, GCO[ ], GBO[ ], and GMO[ ] are the classes of connected outerplanar, biconnected outerplanar, and maximal outerplanar [ ]-drawable graphs, respectively. Gk denotes the class of graphs such that the number of biconnected components sharing a cut-vertex is at most k; Tk is the class of trees whose vertex degree is at most k; T is the class of forbidden trees described in [2].

"... In PAGE 2: ... Table1 : Summarizing the characterization results on the -drawability of outerplanar graphs for 1 2. References [1] P.... ..."

### Table 2. Bicriteria spanning tree results for treewidth-bounded graphs.

"... In PAGE 6: ... As before, the rows are indexed by the budgeted objective. All algorithmic results in Table2 also extend to Steiner trees in a straightforward way. Our results for treewidth-bounded graphs have an interesting application in the context of find- ing optimum broadcast schemes.... In PAGE 19: ...1 Exact Algorithms Theorem 8.1 Every problem in Table2 can be solved exactly in O((n C)O(1))-time for any class of treewidth bounded graphs with no more than k terminals, for fixed k and a budget C on the first objective. The above theorem states that there exist pseudopolynomial-time algorithms for all the bicriteria problems from Table 2 when restricted to the class of treewidth-bounded graphs.... In PAGE 19: ...1 Every problem in Table 2 can be solved exactly in O((n C)O(1))-time for any class of treewidth bounded graphs with no more than k terminals, for fixed k and a budget C on the first objective. The above theorem states that there exist pseudopolynomial-time algorithms for all the bicriteria problems from Table2 when restricted to the class of treewidth-bounded graphs. The basic idea is to employ a dynamic programming strategy.... In PAGE 23: ...7 For the class of treewidth-bounded graphs, there is an FPAS for the (Diame- ter, Total cost, Spanning tree)-bicriteria problem with performance guarantee (1; 1 + ). As mentioned before, similar theorems hold for the other problems in Table2 and all these results extend directly to Steiner trees. 8.... ..."

### Table 2. Bicriteria spanning tree results for treewidth-bounded graphs.

"... In PAGE 6: ... As before, the rows are indexed by the budgeted objective. All algorithmic results in Table2 also extend to Steiner trees in a straightforward way. Our results for treewidth-bounded graphs have an interesting application in the context of find- ing optimum broadcast schemes.... In PAGE 19: ...1 Exact Algorithms Theorem 8.1 Every problem in Table2 can be solved exactly in O((n C)O(1))-time for any class of treewidth bounded graphs with no more than k terminals, for fixed k and a budget C on the first objective. The above theorem states that there exist pseudopolynomial-time algorithms for all the bicriteria problems from Table 2 when restricted to the class of treewidth-bounded graphs.... In PAGE 19: ...1 Every problem in Table 2 can be solved exactly in O((n C)O(1))-time for any class of treewidth bounded graphs with no more than k terminals, for fixed k and a budget C on the first objective. The above theorem states that there exist pseudopolynomial-time algorithms for all the bicriteria problems from Table2 when restricted to the class of treewidth-bounded graphs. The basic idea is to employ a dynamic programming strategy.... In PAGE 23: ...7 For the class of treewidth-bounded graphs, there is an FPAS for the (Diame- ter, Total cost, Spanning tree)-bicriteria problem with performance guarantee (1; 1 + ). As mentioned before, similar theorems hold for the other problems in Table2 and all these results extend directly to Steiner trees. 8.... ..."

### Table 2: Number of in the connectivity graphs

1992

"... In PAGE 8: ... The scanning is an operation of order O#28dn#29 and, for the examples in Figure 2, takes about #0Cve seconds on a DECstation 5000. Table2 gives the number of arcs in the connectivity graphs and the average number of connections per cell. As can be seen, the number of connections is low and appears to be a result of the typical size distribution of slippery cells.... ..."

Cited by 15

### Table 1 - Span of a CREW tree for different levels of decomposition

1995

"... In PAGE 6: .... Zandi, M. Boliek, E.L. Schwartz, M.J. Gormish, A. Keith - 12 September 1995 v List of tables Table1 - Span of a CREW tree for different levels of decomposition.... In PAGE 17: ... For example, with one level of decomposition a CREW tree spans four pixels, with two levels it spans 16, etc. Table1 shows the number of pixels affected by a CREW tree for different levels. 1.... ..."

Cited by 7

### Table 1: Connected regular graphs.

1999

"... In PAGE 6: ...ayreuth.de/markus/reggraphs.html. From this site you can even download various lists and some drawings of regular graphs. Table1 shows results of the program for runs with given number n of vertices and degree k. It contains the number of computed regular graphs, the total number of candidates for the minimality test, the quotient of these two numbers and the CPU-times for computation on a PC Pentium Pro with 200 MHz.... ..."

Cited by 7

### Table 1: Multi-source Spanning Tree Problems and Their Complexity Status

"... In PAGE 20: ... Combining the operations in all possible ways (varying the order of operations and their ranges), we obtain six cost functions. Table1 lists the corresponding decision problems and their complexity status.... In PAGE 22: ...of the corresponding decision problems. We note that tractability of the last three problems in Table1 follows from the fact that there is a point p on the graph (not necessarily a vertex) such a solution spanning tree is the shortest-path single-source p spanning tree of G. References [1] H.... ..."