### Table 1: Numbers of labelled connected (an) and all (An) P4-free chordal graphs with n vertices

2001

Cited by 1

### Table 1: Separating examples between chordal probe graphs and related incomparable classes.

2005

### Table 2: Cycles in Original and Augmented Benchmark Graphs. Results are given for the three different methods of encoding transitivity constraints.

2000

"... In PAGE 10: ... In addition, the edges forming the perimeter of each face F i create a chord-free cycle, giving a total of 2 n + n chord-free cycles. The columns labeled Direct in Table2 show results for enumerating the chord-free cycles for our benchmarks. For each correct microprocessor, we have two graphs: one for which transitivity constraints played no role in the verification, and one (indicated with a t at the end of the name) modified to require enforcing transitivity constraints.... In PAGE 13: ... The graph has N#28N , 1#29 edges and N#28N , 1#29#28N , 2#29=6 chord-free cycles, yielding a total of N#28N , 1#29#28N , 2#29=2=O#28N 3 #29transitivity constraints. The columns labeled Dense in Table2 show the complexity of this method for the benchmark circuits. For the smaller graphs 1#02DLX-C, 1#02DLX-C-t, M 4 and M 5 , this method yields more clauses than direct enumeration of the cycles in the original graph.... In PAGE 14: ... If more than one vertex has minimum degree, we choose one that minimizes the number of new edges added. The columns in Table2 labeled Sparse show the effect of making the benchmark graphs chordal by this method. Observe that this method gives superior results to either of the other two methods.... In PAGE 15: ... One can see that the set of edges forming the border of each face forms a chord-free cycle of M n . As shown in Table2 , many other cycles are also chord-free, e.g.... In PAGE 21: ... Table 4 shows the complexity of the graphs generated by this method for our benchmark cir- cuits. Comparing these with the full graphs shown in Table2 , we see that we typically reduce the number of relational vertices (i.e.... ..."

Cited by 30

### Table 2. Cycles in Original and Augmented Benchmark Graphs. Results are given for the three different methods of encoding transitivity constraints.

2000

"... In PAGE 6: ... Thus there are a61 a24a23 such cycles. The columns labeled Direct in Table2 show results for enumerating the chord- free cycles for our benchmarks. For each correct microprocessor, we have two graphs: one for which transitivity constraints played no role in the verification, and one (in- dicated with a t at the end of the name) modified to require enforcing transitivity constraints.... In PAGE 8: ... The graph has a36a23a54a41a36 a56 a43a58a57 edges and a36a23a54a41a36 a56a51a43a58a57a77a54a41a36 a56 a61a62a57a60a59 a27 chord-free cycles, yielding a total of a36 a54a55a36 a56a51a43a58a57a39a54a55a36 a56 a61 a57 a59a62a61 a32 a1a0 a54a41a36a3a2a58a57 transitivity constraints. The columns labeled Dense in Table2 show the complexity of this method for the benchmark circuits. For the smaller graphs 1a0 DLX-C, 1a0 DLX-Ct, a26 a5a4 and a26 a7a6 , this method yields more clauses than direct enumeration of the cycles in the original graph.... In PAGE 8: ... If more than one vertex has minimum degree, we choose one that minimizes the number of new edges added. The columns in Table2 labeled Sparse show the effect of making the benchmark graphs chordal by this method. Observe that this method gives superior results to either of the other two methods.... In PAGE 11: ... Table 4 shows the complexity of the graphs generated by this method for our bench- mark circuits. Comparing these with the full graphs shown in Table2 , we see that we... ..."

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### Table 2. DESIRE, Constraint Graphs, and Conceptual Graphs

"... In PAGE 15: ... Other elements however, are harder to translate to a Conceptual Graph notation. Table2 provides an overview of the translation of DESIRE elements to Conceptual Graphs. Part of this is discussed in some detail.... ..."

### Table 2. DESIRE, Constraint Graphs, and Conceptual Graphs

"... In PAGE 15: ... Other elements however, are harder to translate to a Conceptual Graph notation. Table2 provides an overview of the translation of DESIRE elements to Conceptual Graphs. Part of this is discussed in some detail.... ..."

### Table 2 DESIRE, Constraint Graphs, and Conceptual Graphs

2002

"... In PAGE 10: ... Other elements however, are harder to translate to a Conceptual Graph notation. Table2 provides an overview of the translation of DESIRE elements to Conceptual Graphs. Part of this is discussed in some detail.... ..."

### Table 2: The Balas-Xue Algorithm and its Variants Balas-Xue Greedy Chordal

2007

"... In PAGE 9: ... Table 1 shows results obtained by solving the maximum independent set problem on some graphs from the Second DIMACS Implementation Chal- lenge (Johnson and Trick, 1996); the times are in seconds, and an asterisk (*) denotes instances in which computer memory was exhausted. Table2 shows results obtained by solving the maximum weight independent set problem on some uniform random graphs with uniformly distributed vertex weights; see Section 7 for details about these graphs. Each line of Table 2 gives the average times and nodes across a sample of 10 graphs with the same edge probability p.... In PAGE 9: ... Table 2 shows results obtained by solving the maximum weight independent set problem on some uniform random graphs with uniformly distributed vertex weights; see Section 7 for details about these graphs. Each line of Table2 gives the average times and nodes across a sample of 10 graphs with the same edge probability p. The range of edges in the graphs is given in the column under jEj.... ..."

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