### TABLE 1. Complexity results for ten famous graph problems when restricted to the classes of graphs discussed in the text. The ten problems are INDEPENDENT SET, CLIQUE, PARTITION INTO CLIQUES, CHROMATIC NUMBER, CHROMATIC INDEX, HAMILTONIAN CIRCUIT, DOMINATING SET, SIMPLE (unweighted) MAX CUT, (unweighted) STEINER TREE IN GRAPHS, and GRAPH ISOMORPHISM. The first nine are known to be NP-complete for general graphs; the complexity of GRAPH ISOMORPHISM for general graphs is a long-standing open problem. The well-known VERTEX COVER problem is not included as its complexity will always be the same as that of INDEPENDENT SET; see [G amp;J, p.54]. The second column gives the com- plexity of determining membership in the given class (and constructing the associated model where appropriate, as in the case of intersection graphs). For a key to the abbreviations used as entries in the table, see the continuation of the table on the next page.

1985

Cited by 159

### Table 3 Results for constructed graphs

"... In PAGE 27: ... At the bottom of the table one can additionally find the average running times and the number of the best known solutions which is twice as high as in the old TS and comprises all instances for the MBCH+TSCS. Table3 presents the results for the constructed graphs. The structure of the heading is the same as in Table 2.... ..."

### Table 3: Overview of methods of graph construction

1992

"... In PAGE 4: ... 5 The graphs and methods compared In this section, we give a comparison between the di erent types of graphs and the methods of construction. In Table3 an overview is given of the methods of construction of graphs described in this paper. For all methods it is supposed an independency model M is given.... In PAGE 4: ... In Table 4, an overview of the properties of the construction methods is given. The name in the rst column refers to the name the rst column of Table3 . In the second column the axioms are given under which the model must be closed to get a map as denoted in the last column.... ..."

### Table 2: Parameters and their distribution of the constructed random graphs.

"... In PAGE 6: ...1 Qualitative and Quantitative Analysis Results This subsection presents analysis results to demonstrate the practical applicability of our approach with respect to both layout quality and runtime performance. The deter- minants of the analyzed graphs are given in Table2 ; they resemble problem properties... ..."

### Table 1: Construction of the conditional path graph

1997

Cited by 4