### Table 1: The complexity of list ranking of graphs.

"... In PAGE 18: ...exist for these three classes of graphs [2]. Vertices u, v in the second row of Table1 denote the internal vertices of a graph, while e is the internal edge of a graph. In the case of polynomial-time instances Table 1 gives the complexity of finding the list ranking number of a graph.... In PAGE 18: ... Vertices u, v in the second row of Table 1 denote the internal vertices of a graph, while e is the internal edge of a graph. In the case of polynomial-time instances Table1 gives the complexity of finding the list ranking number of a graph. References [1] H.... ..."

### Table 1: The complexity of list ranking of graphs.

"... In PAGE 18: ...exist for these three classes of graphs [2]. Vertices u, v in the second row of Table1 denote the internal vertices of a graph, while e is the internal edge of a graph. In the case of polynomial-time instances Table 1 gives the complexity of finding the list ranking number of a graph.... In PAGE 18: ... Vertices u, v in the second row of Table 1 denote the internal vertices of a graph, while e is the internal edge of a graph. In the case of polynomial-time instances Table1 gives the complexity of finding the list ranking number of a graph. References [1] H.... ..."

### Table 1: Subgraph isomorphism problem: complexity for a xed pattern H and for an input graph restricted to some class of graphs.

### Table 1: Relative complexity for certain problems restricted to the graph classes I, UD, P, and TL.

in Improper

"... In PAGE 3: ...Table1 for a summary of what is known about these problems, comparing the restrictions to interval graphs, to unit disk graphs, to planar graphs, to disk graphs and to weighted induced subgraphs of the triangular lattice. Later, we shall be able to add two rows to this table that correspond to k-IMPROPER CHROMATIC NUMBER and MAX k-DEPENDENT SET.... ..."

### Table 1.1: Relative complexity for certain problems restricted to the graph classes I, UD and P.

2005

### Table 1. Summary of the complexity results (GI means graph isomorphism).

"... In PAGE 13: ... 4. Conclusions The main results of this paper are on the one hand the graph isomorphism com- pleteness of the general (combinatorial) polytope isomorphism problem and, on the other hand, the fact that this problem can be solved in polynomial time if the dimensions of the polytopes are bounded by a constant (see Table1 for an overview of the complexity results and Fig. 6 for a sketch of the complexity theoretic land- scape considered in this paper).... In PAGE 14: ... It may be that one can turn our algorithm into a computer code that becomes compatible with nauty for checking combinatorial polytope isomorphism. The remaining two open entries in Table1 concern the complexity of the graph isomorphism problem restricted to graphs of arbitrary (or simplicial) polytopes of bounded dimensions. A polynomial time algorithm for this problem would perhaps not be as interesting as the potential result that the problem is graph isomorphism complete, because the latter result would show that the class of graphs of polytopes... ..."

Cited by 4

### Table 1. Summary of the complexity results (GI means graph isomorphism).

"... In PAGE 13: ... 4. Conclusions The main results of this paper are on the one hand the graph isomorphism com- pleteness of the general (combinatorial) polytope isomorphism problem and, on the other hand, the fact that this problem can be solved in polynomial time if the dimensions of the polytopes are bounded by a constant (see Table1 for an overview of the complexity results and Fig. 6 for a sketch of the complexity theoretic land- scape considered in this paper).... In PAGE 14: ... It may be that one can turn our algorithm into a computer code that becomes compatible with nauty for checking combinatorial polytope isomorphism. The remaining two open entries in Table1 concern the complexity of the graph isomorphism problem restricted to graphs of arbitrary (or simplicial) polytopes of bounded dimensions. A polynomial time algorithm for this problem would perhaps not be as interesting as the potential result that the problem is graph isomorphism complete, because the latter result would show that the class of graphs of polytopes... ..."

Cited by 4

### Table 1. Summary of the complexity results (GI means graph isomorphism).

"... In PAGE 13: ... 4. Conclusions The main results of this paper are on the one hand the graph isomorphism com- pleteness of the general (combinatorial) polytope isomorphism problem and, on the other hand, the fact that this problem can be solved in polynomial time if the dimensions of the polytopes are bounded by a constant (see Table1 for an overview of the complexity results and Fig. 6 for a sketch of the complexity theoretic land- scape considered in this paper).... In PAGE 14: ... It may be that one can turn our algorithm into a computer code that becomes compatible with nauty for checking combinatorial polytope isomorphism. The remaining two open entries in Table1 concern the complexity of the graph isomorphism problem restricted to graphs of arbitrary (or simplicial) polytopes of bounded dimensions. A polynomial time algorithm for this problem would perhaps not be as interesting as the potential result that the problem is graph isomorphism complete, because the latter result would show that the class of graphs of polytopes... ..."

Cited by 4

### Table 2: Shapes of complexity graphs

1993

"... In PAGE 54: ... Therefore, it is interesting to investigate in which of the cases not only the worst-case complexity, but also the average-case complexity scales linearly with the complexity of the domain. Table2 shows which graphs of the average-case complexity deviate from the corre- sponding graphs of the worst-case complexity. The rst entry is always the shape of the graph for the worst-case complexity (as stated above, i.... ..."

Cited by 39

### Table 2: Shapes of complexity graphs

1993

"... In PAGE 54: ... Therefore, it is interesting to investigate in whichof the cases not only the worst-case complexity, but also the average-case complexity scales linearly with the complexity of the domain. Table2 shows which graphs of the average-case complexity deviate from the corre- sponding graphs of the worst-case complexity. The #0Crst entry is always the shape of the graph for the worst-case complexity #28as stated above, i.... ..."

Cited by 39