In this note, we use a reduction by Cornaz and Jost from the graph (max-)coloring problem to the maximum (weighted) stable set problem in order to characterize new graph classes where the graph coloring problem and th...
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In this note, we use a reduction by Cornaz and Jost from the graph (max-)coloring problem to the maximum (weighted) stable set problem in order to characterize new graph classes where the graph coloring problem and the more general max-coloring problem can be solved in polynomialtime. (C) 2013 Elsevier B.V. All rights reserved.
The problem of determining a minimum total dominating set along with several closely related problems has been investigated remarkably. For general graphs, the total dominating set problem is computationally intracta...
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The problem of determining a minimum total dominating set along with several closely related problems has been investigated remarkably. For general graphs, the total dominating set problem is computationally intractable. Actually, it is an NP-complete problem. Thus, it is very unlikely that this problem can be solved by an efficient algorithm whose running time is bounded by a polynomial in the size of the input. The total dominating set problem also is NP-complete for special classes of graphs, such as bipartite graphs, split graphs, and undirected path graphs. Interval graphs represent intersecting intervals on the line. An O(n-squared) timealgorithm for finding a minimum total dominating set in an interval graph by reducing it to a shortest path problem on an appropriate acyclic directed network is presented. The type of reduction used can easily be modified to work in the weighted case also.
A subset of edges J subset of or equal to E(G) in a undirected graph G is called a join if at most half the edges of each cycle of G are contained in J. In this paper we consider the problem of finding a join of maxim...
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A subset of edges J subset of or equal to E(G) in a undirected graph G is called a join if at most half the edges of each cycle of G are contained in J. In this paper we consider the problem of finding a join of maximum weight: given a graph G and an edge weighting c:E(G) --> R, find a join of maximum weight. We show that the problem is NP-hard even in the case of 0, 1-weights, which answers a question of A. Frank in the negative. We also show that in the case of series-parallel graphs and arbitrary weights, the problem can be solved in time 0(n(3)), where n is the number of vertices in G. (C) 2001 Elsevier Science B.V. All rights reserved.
In this correspondence, we study the problem of finding optimal reconfiguration strategies for a class of reconfigurable fault- tolerant computer systems in which there is no repair in failed components. The problem o...
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In this correspondence, we study the problem of finding optimal reconfiguration strategies for a class of reconfigurable fault- tolerant computer systems in which there is no repair in failed components. The problem of finding optimal reconfiguration strategies consists of determining, for each failed state of the system, the operational state into which the system should reconfigure itself. We presented a stochastic model for the above class of reconfigurable computer systems. Based on this model, we construct a polynomial-time algorithm for finding optimal reconfiguration strategies.
In classical machine scheduling problems the jobs are independent in general. Motivated by some special processing environments, this paper studies a model of scheduling problems with constraints that some groups of j...
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In classical machine scheduling problems the jobs are independent in general. Motivated by some special processing environments, this paper studies a model of scheduling problems with constraints that some groups of jobs have to be processed contiguously. It turns out that the feasibility of these constrained scheduling problems is equivalent to the recognition of interval hypergraphs. For this new model, two examples of single machine scheduling problems with polynomial-time algorithms are taken as a start. (c) 2013 Elsevier B.V. All rights reserved.
A clique-coloring of a graph G is a coloring of the vertices of G so that no maximal clique of size at least two is monochromatic. The clique-hypergraph, H(G), of a graph G has V (G) as its set of vertices and the max...
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A clique-coloring of a graph G is a coloring of the vertices of G so that no maximal clique of size at least two is monochromatic. The clique-hypergraph, H(G), of a graph G has V (G) as its set of vertices and the maximal cliques of G as its hyperedges. A (vertex) coloring of H(G) with no monochromatic hyperedge is a clique-coloring of G. The clique-chromatic number of G is the least number of colors for which G admits a clique-coloring. Every planar graph has been proved to be 3-clique-colorable and every claw-free planar graph, different from an odd cycle, has been proved to be 2-clique-colorable. In this paper we first generalize the result of planar graphs to K-5-minor-free graphs. Furthermore, we generalize the result of claw-free planar graphs to K-5-subdivision-free graphs and give a polynomial-time algorithm to find a 2-clique-coloring of K-5-subdivision-free graphs. (C) 2015 Elsevier B.V. All rights reserved.
Discrete tomography focuses on the reconstruction of functions from their line sums in a finite number d of directions. In this paper we consider functions f : A -> R where A is a finite subset of Z(2) and R an int...
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Discrete tomography focuses on the reconstruction of functions from their line sums in a finite number d of directions. In this paper we consider functions f : A -> R where A is a finite subset of Z(2) and R an integral domain. Several reconstruction methods have been introduced in the literature. Recently Ceko, Pagani and Tijdeman developed a fast method to reconstruct a function with the same line sums as f. Up to here we assumed that the line sums are exact. Some authors have developed methods to recover the function f under suitable conditions by using the redundancy of data. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than d/2 errors can be corrected and that this bound is the best possible. Moreover, we prove that if it is known that the line sums in k given directions are correct, then the line sums in every other direction can be corrected provided that the number of wrong line sums in that direction is less than k/2.
The Eulerian closed walk problem in a digraph is a well-known polynomial-time solvable problem. In this paper, we show that if we impose the feasible solutions to fulfill some precedence constraints specified by paths...
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The Eulerian closed walk problem in a digraph is a well-known polynomial-time solvable problem. In this paper, we show that if we impose the feasible solutions to fulfill some precedence constraints specified by paths of the digraph, then the problem becomes NP-complete. We also present a polynomial-time algorithm to solve this variant of the Eulerian closed walk problem when the set of paths does not contain some forbidden structure. This allows us to give necessary and sufficient conditions for the existence of feasible solutions in this polynomial-time solvable case. (C) 2012 Published by Elsevier B.V.
We study the vertex coloring problem in classes of graphs defined by finitely many forbidden induced subgraphs. Of our special interest are the classes defined by forbidden induced subgraphs with at most 4 vertices. F...
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We study the vertex coloring problem in classes of graphs defined by finitely many forbidden induced subgraphs. Of our special interest are the classes defined by forbidden induced subgraphs with at most 4 vertices. For all but three classes in this family we show either NP-completeness or polynomial-time solvability of the problem. For the remaining three classes we prove fixed-parameter tractability. Moreover, for two of them we give a 3/2 approximation polynomialalgorithm. (C) 2015 Elsevier B.V. All rights reserved.
Motivated by the connection with the genus of unoriented alternating links, Jin et al. (Acta Math Appl Sin Engl Ser, 2015) introduced the number of maximum state circles of a plane graph G, denoted by , and proved tha...
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Motivated by the connection with the genus of unoriented alternating links, Jin et al. (Acta Math Appl Sin Engl Ser, 2015) introduced the number of maximum state circles of a plane graph G, denoted by , and proved that H is a spanning subgraph of , where e(H), c(H) and v(H) denote the size, the number of connected components and the order of H, respectively. In this paper, we show that for any (not necessarily planar) graph G, can be achieved by the spanning subgraph H of G whose each connected component is a maximal subgraph of G with two edge-disjoint spanning trees. Such a spanning subgraph is proved to be unique and we present a polynomial-time algorithm to find such a spanning subgraph for any graph G.
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