Gavril, F. Algorithms on clique separable graphs, 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....subgraphs using clique separators. The result states that if each subgraph can be colored using at most k colors, then the entire graph can be colored in k colors by combining the coloring of subgraphs [46] A clique separators is a completely connected subgraph whose removal disconnects the graph [19]. Each subgraph includes the clique separator, and a renaming of registers for the clique separator nodes might be needed when merged with other subgraphs. In Tarjan s work, the entire interference graph is constructed all at once, and clique separators identified later. In Gupta et al. clique ....

F. Gavril. Algorithms on clique separable graph. 19:159 165, 1977.

....giving an explicit construction rule: Find basic graphs B C which are irreducibel with respect to a set of graph operations O such that G 2 C i G 2 B or G = G 1 G 2 with G 1 ; G 2 2 C; 2 O. The class of Meyniel graphs admits such a constructive characterization [4] Clique separable graphs [7] are graphs whose connected subgraphs without any clique cutset are complete k partite or the complete join of a connected bipartite graph and a clique. In the case of (anti)critically perfect graphs, the hope was that (anti)critically perfect line graphs are the basic graphs and all other ....

F. Gavril, Algorithms on Clique Separable Graphs, Discrete Math. 19 (1977) 159-165.

....4. Let (X; T ) be a tree decomposition of a graph G and X i ; X j 2 X be two sets connected by an edge in T . If neither X i X j nor X j X i then X i X j is a separator in G. The last notions of this section concern decompositions of graphs based on clique separators introduced by Gavril [10] and examined among others by Tarjan [22] Let us denote these decompositions by clique decompositions in order to distinguish them from tree decompositions of Definition 3. A clique decomposition can be represented by a binary tree whose leaves are atoms (graphs having no clique separators) and ....

F. Gavril. Algorithms on clique separable graphs. Disc. Math., 19:159--165, 1977.

....of bounded size [1, 2, 3, 4, 12] A decomposition of this type can be found in linear time [5, 12] however, the huge constants involved in these algorithms do not make them of much practical use. A closely related but somewhat di#erent approach was surveyed in [19] In that paper (see also [8]) it is shown that for many classes of graphs (for example chordal graphs, clique separable graphs, and edge intersection graphs of paths in a tree (EPTgraphs) a decomposition by clique separators is possible, and it is illustrated that such a decomposition can also be used to solve e#ciently ....

F. GAVRIL, Algorithms on clique separable graphs, Discrete Math., 19 (1977), pp. 159--165.

.... graph classes have been characterized by the structure of their clique separators, among them chordal graphs [Di 61, HS 58] path graphs (the intersection graphs of paths in a tree) MW 86] and Gallai graphs (graphs where every odd cycle of length five or more contains two non crossing chords) Ga 77] One of the original motivations for studying the clique separator decomposition is related to the problem of recognizing perfect graphs [Wh 84] If X is a clique separator of G and removing X leaves connected components with vertex sets V 1 ; V 2 ; V k , then G is perfect if and only ....

Gavril, F. Algorithms on Clique Separable Graphs, Discrete Mathematics 19 (1977), pp. 159-165.

.... proven to be perfectly contractile include the triangulated graphs [19] which are contained in all three of the classes mentioned above) the comparability graphs [19] which are perfectly orderable) the parity and i triangulated graphs [8] which are Meyniel) and the clique separable graphs [18]. For an alternative proof that these last three classes are perfectly contractile see [5] Having proved that all these graphs are perfectly contractile, we would like to design fast and simple optimization algorithms which take advantage of the contraction sequences to optimally colour and find ....

A. Gavril, Algorithms on clique-separable graphs, Discrete Math., 19 (1977) 159--165.

....of bounded size [1, 2, 3, 4, 12] A decomposition of this type can be found in linear time [5, 12] however the huge constants involved in these algorithms do not make them of much practical use. A closely related, but somewhat different approach was surveyed in [19] In this paper (see also [8]) it is shown that for many classes of graphs (for example chordal graphs, clique separable graphs and edge intersection graphs of paths in a tree or EPT graphs) a decomposition by clique separators is possible, and it is illustrated that such a decomposition can also be used to solve efficiently ....

Gavril, F., Algorithms on clique separable graphs, Discrete Mathematics 19 (1977), pp. 159--165.

....naturally from the way an algebraic compiler builds the target image and allows the compiler to independently color subgraphs and reuse space once a subgraph has been colored. Since this is not naturally achieved in conventional compilers, Gupta, Soffa, and Ombres [15] use clique separators [13, 23] to decompose a register interference graph into subgraphs that can be independently colored and combined. The algorithm of Gupta et.al. needs to be judicious in its choice of clique separators. On the other hand, the algebraic compiler, during the course of building the target image, ....

F. Gavril. Algorithms on clique-separable graphs. Discrete Mathematics, 19:159--165, 1977.

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Gavril, F. Algorithms on clique separable graphs, 1977.

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F. Gavril, Algorithms on clique-separable graphs, Discrete Math. 19 (1977) 159--165.

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