The minimum weight feedback vertex set problem (FVS) on series-parallel graphs can be solved in O(n) time by dynamic programming. This solution, however, does not provide a "nice" certificate of optimality. ...
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The minimum weight feedback vertex set problem (FVS) on series-parallel graphs can be solved in O(n) time by dynamic programming. This solution, however, does not provide a "nice" certificate of optimality. We prove a min-max relation for FVS on series-parallel graphs with no induced subdivision of K-2,K-3 (a class of graphs containing the outerplanar graphs), thereby establishing the existence of nice certificates for these graphs. Our proof relies on the description of a complete set of inequalities defining the feedback vertex set polytope of a series-parallel graph with no induced subdivision of K-2,K-3. We also prove that many of the inequalities described are facets of this polytope. (C) 2009 Elsevier B.V. All rights reserved.
Given a network with n vertices and m edges where each edge has an independent operational probability, we are interested in finding a vertex of the network whose expected number of reachable vertices is maximum. Such...
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Given a network with n vertices and m edges where each edge has an independent operational probability, we are interested in finding a vertex of the network whose expected number of reachable vertices is maximum. Such a vertex is called a most reliable sourer of the network. This problem was studied by Melachrinoudis and Helander (1996) where an O(n(2)) time algorithm was proposed when the given network is a tree. In a more recent paper, Xue presented an O(n) time algorithm for this problem when the given network is a tree, in this paper, we present an O(n) time algorithm for computing the most reliable source on series-parallel graphs, using their embeddings in 2-trees. (C) 1998-Elsevier Science B.V. All rights reserved.
This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series-para...
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This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series-parallel graph. It is shown that for the general linear problem to minimize the makespan, polynomial algorithms exist. It is also shown that for the proportional linear problem of minimization of the total weighted completion time, polynomial algorithms exist, too. (C) 2007 Elsevier Ltd. All rights reserved.
Given a weighted graph (G, l) and its associated moduli space M(G, l), then a sufficient condition is provided which ensures that M(G, l) is a smooth manifold whenever G is a series-parallel graph. (C) 2014 Elsevier B...
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Given a weighted graph (G, l) and its associated moduli space M(G, l), then a sufficient condition is provided which ensures that M(G, l) is a smooth manifold whenever G is a series-parallel graph. (C) 2014 Elsevier B.V. All rights reserved.
A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. We find an asymptotics for the number of labeled connected series-parallel tetracyclic graphs with a large numbe...
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In this paper, we describe the circuit polytope on series-parallel graphs. We first show the existence of a compact extended formulation. Though not being explicit, its construction process helps us to inductively pro...
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In this paper, we describe the circuit polytope on series-parallel graphs. We first show the existence of a compact extended formulation. Though not being explicit, its construction process helps us to inductively provide the description in the original space. As a consequence, using the link between bonds and circuits in planar graphs, we also describe the bond polytope on series-parallel graphs. (C) 2015 Elsevier B.V. All rights reserved.
The problems of recognizing series-parallel graphs, outerplanar graphs, and generalized series-parallel graphs have been studied separately in the past. Efficient algorithms have been presented. However, none of the a...
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The problems of recognizing series-parallel graphs, outerplanar graphs, and generalized series-parallel graphs have been studied separately in the past. Efficient algorithms have been presented. However, none of the algorithms are certifying. A certifying algorithm generates, in addition to its answer, a certificate that can be used by a checker (a separate algorithm) to verify the correctness of the answer. The certificate is positive if the answer is 'yes', and is negative if the answer is 'no'. In this paper, an O(|E| + |V |)-time certifying algorithm that simultaneously determines if a graph G = (V, E) is series- parallel, outerplanar, or generalized series-parallel is presented. The positive certificates are a construction sequence for constructing G if G is series-parallel, a generalized construction sequence for constructing G if G is generalized series-parallel but not series-parallel, and the edge set of the exterior boundary of an outerplanar embedding of G if G is outerplanar. The negative certificates are forbidden subgraphs or forbidden structures of G. All these certificates are generated by making only one pass over G after a preprocessing step decomposing G into its biconnected components.(c) 2022 Elsevier B.V. All rights reserved.
Bouchet conjectured in 1983 that each signed graph that admits a nowhere-zero flow has a nowhere-zero 6-flow. We prove that the conjecture is true for all signed series-parallel graphs. Unlike the unsigned case, the r...
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Bouchet conjectured in 1983 that each signed graph that admits a nowhere-zero flow has a nowhere-zero 6-flow. We prove that the conjecture is true for all signed series-parallel graphs. Unlike the unsigned case, the restriction to series-parallel graphs is nontrivial;in fact, the result is tight for infinitely many graphs.
In this paper we give an algorithm to generates all series-parallel graphs with at most m edges. This algorithm generate each series-parallel graph in constant time on average.
In this paper we give an algorithm to generates all series-parallel graphs with at most m edges. This algorithm generate each series-parallel graph in constant time on average.
Suppose G is a series-parallel graph, We prove that if G has odd girth at least 6k - 1 then chi(c)(G) less than or equal to 8k/(4k - 1);if G has odd girth at least 6k + 1 then chi(c)(G) less than or equal to (4k + 1)/...
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Suppose G is a series-parallel graph, We prove that if G has odd girth at least 6k - 1 then chi(c)(G) less than or equal to 8k/(4k - 1);if G has odd girth at least 6k + 1 then chi(c)(G) less than or equal to (4k + 1)/2k;if G has odd girth at least 6k + 3 then chi(c)(G) less than or equal to (4k + 3)/(2k + 1). (C) 2002 Elsevier Science B.V. All rights reserved.
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