Greenlaw, R. -- Petreschi, R.: Cubic graphs, ACM Computing Surveys, 27(4), pp. 471-495, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... s (G) 10. We also note that the result given in [NOdM01] yields the same upper bound. However, it is possible to slightly improve this bound to 9. First, we 10 give some de nitions that will lead us to Proposition 4 : for any cubic graph G, an H expansion of G consists in the following (cf. [GP95]) let e 1 = v2; v4) and e 2 = v 3 ; v 5 ) be two edges in G. The H expansion of G with respect to e 1 and e 2 is the following transformation : 1) delete edges e 1 and e 2 , 2) add two new vertices v 0 and v 1 and the edge (v 0 ; v 1 ) and add either 3a) edges (v 0 ; v 2 ) v 1 ; v 4 ) v 0 ....

R. Greenlaw and R. Petreschi. Cubic graphs. ACM Computing Surveys, 27(4):471-495, 1995.

....paper can have parallel edges. We use the term simple graphs to denote the ones without parallel edges. A graph is cubic if every vertex has degree three. A graph is subcubic if none of its vertices has degree more than three [22] Subcubic graphs are also called at most cubic in the literature [16]. We prefer the former term since it reminds us of the fact that a subcubic graph is always an induced subgraph of some cubic graph. And furthermore, a simple subcubic graph is an induced subgraph of some simple cubic graph. Subcubic graphs are interesting and important theoretically and in ....

....prefer the former term since it reminds us of the fact that a subcubic graph is always an induced subgraph of some cubic graph. And furthermore, a simple subcubic graph is an induced subgraph of some simple cubic graph. Subcubic graphs are interesting and important theoretically and in practice [16, 8, 3] for several reasons. First, graphs of maximum degree three are often the borderline cases between the hard and easy problems. Most NP hard problems and some APX hard problems do not become easier even when restricted to such graphs [15, 16, 1, 24, 25] but become polynomial time solvable for ....

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Raymond Greenlaw and Rossella Petreschi. Cubic graphs. ACM Computing Surveys, 27(4):471-495, 1995.

....recoloring. Lovasz s algorithm colors each biconnected component separately, then puts these colorings together by appropriately permuting colors in each component. Our algorithm never recolors. A class of graphs that has proven itself to be of special interest is the class of subcubic graphs [7]. References [6, 12] show that a simple decomposition principle for subcubic graphs gives efficient algorithms for solving various coloring problems on them. We will exploit this principle to obtain a version of our algorithm that is specialized to subcubic Brooks graphs and that is simpler than ....

Raymond Greenlaw and Rossella Petreschi. Cubic graphs. ACM Computing Surveys, 27(4):471--495, 1995.

....recoloring. Lovasz s algorithm colors each biconnected compo nent separately, then put these colorings together by appropriately permuting colors in each component. Our algorithm never recolors. A class of graphs that has proven itself to be of special interest is the class of subcubic graphs [9]. References [10, 11] show that a simple decomposition principle for subcubic graphs give e#cient algorithms for solving various coloring problems on them. We will exploit this principle to obtain a version of our algorithm that is specialized to subcubic Brooks graphs and that is simpler than the ....

Greenlaw, R., Petreschi, R.: Cubic graphs. ACM Computing Surveys 27 (1995) 471--495

....address: skulratt cs.colorado.edu (San Skulrattanakulchai) Preprint submitted to Elsevier Preprint In fact, 7] shows that the problem remains NP complete even when restricted to cubic graphs, those graphs whose every vertex is incident with exactly three edges. As observed in the survey paper [6] on cubic graphs, cubic graphs often seem to be the simplest class of graphs for which a problem remains as di#cult to solve as on a general graph. By studying the problem when restricted to cubic graphs we may gain insight into why the problem is di#cult. Specific subclasses of cubic graphs have ....

R. Greenlaw and R. Petreschi, Cubic graphs, ACM Computing Surveys 27, 4 (1995) 471--495.

....have a great relevance both from the theoretical and practical point of view. Despite the apparent simplicity of cubic and at most cubic graphs, several NP hard graph problems remain NP hard even if restricted to these classes of graphs, but become polynomial time solvable for graphs of degree 2 [10, 12]. Since one can be almost certain that NP hard problems cannot be efficiently solved, one has to restrict oneself to compute approximate solutions. Therefore it would be desirable to identify if and how much boundedness of the graph degree is helpful in approximation. It is well known that the ....

R. Greenlaw and R. Petreschi, Cubic graphs, ACM Computing Surveys 27, 471--495, 1995. 8

.... Gamma Gamma Gamma n n Figure 1: An example of optimal constrained solution of cardinality greater than jV j=2 3 MIDS in at Most Cubic Graphs Despite the apparent simplicity of cubic and at most cubic graphs, many graph problems are no easier to solve, when restricted to them (see [4] for a complete survey on cubic graphs) Nevertheless, at most) cubicity often allows to achieve better approximation performance for many NP hard graph problems. In the following we focus on cubic and at most cubic graphs, and give a 2 approximate heuristic for MIDS 3. Then, we show that for ....

R. Greenlaw and R.Petreschi, Cubic Graphs, to appear in ACM Computing Surveys, 1995.

....to three) is considered in this paper. The motivation is that cubic graphs are at the boundary between the difficult and the solvable problems in graphs. In fact several NP hard problems remain NP hard if restricted to cubic graphs, but become polynomial time solvable for graphs of degree two [18]. In particular, the APX hardness of MAX IND SET on cubic graphs has been recently demonstrated in [4] An instance of MAX IND SET is represented as a logic formula and transformed into an instance of Maximum 4 ary Conjunctive Constraint Satisfiability (MAX 4 CCSP) in the following way. To each ....

R. Greenlaw and R. Petreschi, "Cubic graphs," ACM Computing Surveys 27 (1995), 471--495.

....(t 1 ) Figure 1: Interaction between two particles. Furthermore, cubic graphs have been widely studied by many researchers, since they seem to be a threshold class of graphs, in the sense that they are the simplest graphs for which several fundamental problems are as di cult as in the general case [5, 14]. Several results on orthogonal drawing of cubic graphs have been presented [2, 6, 7, 11, 17, 18, 19, 20, 22] However, none of the cited papers provides experimental results, although the interest in experimentally testing the performance of graph drawing algorithms has increased in the last ....

R.Greenlaw, and R.Petreschi. Cubic graphs. ACM Computing Surveys, 27 (4):471-495, 1995.

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Greenlaw, R. -- Petreschi, R.: Cubic graphs, ACM Computing Surveys, 27(4), pp. 471-495, 1995.

No context found.

Greenlaw, R. -- Petreschi, R.: Cubic graphs, ACM Computing Surveys, 27(4), pp. 471-495, 1995.

No context found.

Greenlaw, R. -- Petreschi, R.: Cubic graphs, ACM Computing Surveys, 27(4), pp. 471-495, 1995.

No context found.

R. Greenlaw and R. Petreschi, "Cubic graphs," ACM Computing Surveys 27 (1995), 471--495.

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