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An independent (or, stable) set in G is a set V V such that for any u, v V , (u, v) E Note that a proper multicoloring of G is essentially a covering of G with stable sets; each stable set of nodes corresponds to a color and a node v appears in exactly w(v) such sets The weighted chromatic number of a weighted graph (G, w), denoted (G, w), is the smallest number m such that there exists a multicoloring of G of span m, ie, (G, w) is the optimal number of colors required to properly multicolor G Let the weight of a maximal clique in (G, w) be defined as the sum of the weights of the nodes belonging to the clique; note that when G is a hexagon graph, the only maximal cliques are isolated nodes, edges, or triangles.

and low levels of functioning in many areas of life (e.g., schizophrenia). Although this tripartite model is both theoretically heuristic and clinically useful, it is important not to overgeneralize regarding differences among different levels of functioning. There are great variations in both severity and chronicity within a given level (e.g., certain neuroses may be more debilitating than an ostensibly more severe personality disorder). In addition, there is substantial comorbidity both within and between levels so that a disordered individual is likely to show multiple forms of psychopathology (Bornstein, 1998; Costello, 1995). As Table 5.5 shows, all three dimensions of intrapsychic dysfunction low ego strength, maladaptive defenses, and dysfunctional introjects can be mapped onto the tripartite psychopathology model. In this respect, the model represents an integrative framework that links different psychodynamic processes and connects the psychoanalytic model with contemporary diagnostic research. Although the term neurosis is rarely used today in mainstream psychopathology research, perusal of contemporary diagnostic frameworks (including the DSM-IV; APA, 1994) con rms that the tripartite model has had a profound in uence on the way practitioners conceptualize and organize psychological disorders (see also Masling & Bornstein, 1994, and Millon, 1996, for discussions of this issue). PSYCHOANALYSIS AND CONTEMPORARY PSYCHOLOGY: RETROSPECT AND PROSPECT Psychodynamic models of personality occupy a unique place in contemporary psychology. On the one hand, they continue to be roundly criticized perceived by those within and outside the discipline as untested and untestable and denigrated by skeptics as a quasi-phrenological pseudoscience that has hindered the progress of both scienti c and clinical psychology. On the other hand, Freud s theory continues to fascinate many, occupying a central place in undergraduate and graduate psychology texts and in uencing in myriad ways our

The weighted clique number, denoted (G, w) is the maximum weight of any maximal clique in the graph The weighted chromatic number and clique number of a call graph are defined in an analogous fashion For integers k 1, we define the k-locality of a node v to be the induced subgraph consisting of those nodes in G whose graph distance from v is less than or equal to k Given G = (V, E), the graph Gr = (V, E ) is defined by E = E E2 Er 1 Thus any pair of nodes at distance i < r in G is connected by an edge in Gr The problem of channel assignment in a weighted graph (G,w) with reuse distance r is thus the same as multicoloring the graph Gr.

The unweighted clique number of Gr is the maximum size of any clique in Gr, and is denoted (Gr) Similarly, the chromatic number of Gr, the minimum number of colors needed to color Gr, is denoted by (Gr) It is known that when G is a hexagon graph, (Gr) = (Gr) (see Section 453), and an optimal coloring can be computed in polynomial time We assume that such an optimal coloring of the graph Gr is available; thus, every node in Gr is assigned a color from the set {1, 2, , (Gr)} If G is a hexagon graph, we say that G2 is a square graph Figure 41 shows a base coloring with red, blue, and green (r, b, and g) colors for a hexagon graph It is easy to see that a square graph can be base colored with seven colors; Figure 4.

and 0 if it is even. This is useful for setting alternating background colors with a CSS, for example use code such as class= commentbg<MTSimpleCommentOdd> and then have CSS classes named commentbg0 and commentbg1 .