### Table 7: Performance indices for the training and the test phase in example 5.2

"... In PAGE 18: ... Through a random sampling of the state space a data set with 7500 different example is generated, being NT = 5000 and NE = 2500. Table7 shows the performance indices obtained during the training and the test phase, together with the number of rules generated. The HC procedure trained for the operating system state y = 1 produces 21 minimal paths, ... ..."

### Table 3: Relations among inductivity, clique number, and chromatic number of the interference graph.

"... In PAGE 13: ... radii FIRST-FIT STRIP SL RD DD LG arbitrary 5 5 N/A N/A N/A uniform 3 5 3 3 3 We also obtain relations among the inductivity, the clique number, and the chromatic number of the interference graph. Table3 summarizes the upper bounds on the pairwise ratios of these parameters. Table 3: Relations among inductivity, clique number, and chromatic number of the interference graph.... ..."

### Table 3. Statistics on maximal cliques and chromatic numbers for the initial interference graphs constructed by AS and OS.

"... In PAGE 8: ... 6.2 Interference Graphs Table3 compares AS and OS in terms of the initial interference graphs, i.... In PAGE 8: ... Statistics on maximal cliques and chromatic numbers for the initial interference graphs constructed by AS and OS. By comparing Column 4 of Table 1 to Columns 3 and 5 in Table3 , we find that the chromatic number, i.e.... In PAGE 8: ... This indicates clearly that the data set of a program can be successfully placed in an SPM with a size that is much smaller than that of the data set. From Columns 3 and 5 in Table3 , we can also compare AS and OS in terms of the chromatic numbers of their initial interfer- ence graphs. For each benchmark, the chromatic number for AS is significantly smaller than that for OS.... ..."

### Table 5.2: Circular chromatic number of small cubic graphs of girth 9

### Table 5.5: Circular chromatic number of small cubic graphs of girth 6

### Table 5.6: Circular chromatic number of small cubic graphs of girth 8

### Table 1. A new exact algorithm for the computation of the chromatic number of a graph G.

"... In PAGE 3: ...- 3 - A description of the new exact algorithm is given in Table1 . We have used the following notations.... ..."

### Table 1: Optimal upper bounds for the clique number, inductiveness, and chromatic number of the square of a chordal / non-chordal outerplanar graph G.

2004

"... In PAGE 4: ... We examine in detail the low-degree cases, lt; 7, and derive best possible upper bounds on the maximum clique and chromatic numbers, as well as inductiveness of squares of outerplanar graphs. These bounds are illustrated in Table1 . We treat the special case of chordal outerplanar graphs separately, and further classify all chordal outerplanar graphs G for which the inductiveness of G2 exceeds or the clique or chromatic number of G2 exceed + 1.... In PAGE 17: ...orollary 4.10 together with Theorems 4.3 and 4.5 complete the proof of Theorem 4.1 as well as the entries in Table1 in the chordal case for 2 f2; 3; 4; 5; 6g. Observation 4.... ..."

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### Table 1: Optimal upper bounds for the clique number, inductiveness, and chromatic number of the square of a chordal / non-chordal outerplanar graph G.

### Table 2. Results for some DIMACS benchmark problems name of number of number of chromatic size of backtracks backtracks

"... In PAGE 8: ...onsidered DSJC125.1 which has 125 vertices and an edge density 0.1. The results are reported in Table2 . It can be observed that Myc graphsare critical and there is therefore no advantage in using our algorithm instead of Exact for this category of graphs.... ..."

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