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Quick but Odd Growth of Cacti
"... Let F be a family of graphs. Given an input graph G and a positive integer k, testing whether G has a ksized subset of vertices S, such that G \S belongs to F, is a prototype vertex deletion problem. These type of problems have attracted a lot of attention in recent times in the domain of parameter ..."
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of parameterized complexity. In this paper, we study two such problems; when F is either a family of cactus graphs or a family of oddcactus graphs. A graph H is called a cactus graph if every pair of cycles in H intersect on at most one vertex. Furthermore, a cactus graph H is called an odd cactus, if every cycle
On graphtransverse matching problems
"... photocopying or other means, without the permission of the author. ii On graphtransverse matching problems by ..."
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photocopying or other means, without the permission of the author. ii On graphtransverse matching problems by
Transversal, Split Vertex Deletion and Almost 2SAT, and an O∗(1.5214k)
"... We investigate the parameterized complexity of Vertex Cover parameterized by the difference between the size of the optimal solution and the value of the linear programming (LP) relaxation of the problem. By carefully analyzing the change in the LP value in the branching steps, we argue that combini ..."
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exponentially with k. We proceed to show that a more sophisticated branching algorithm achieves a runtime of O∗(2.3146k). Following this, using known and new reductions, we give O∗(2.3146k) algorithms for the parameterized versions of Above Guarantee Vertex Cover, Odd Cycle
VertexColored Graphs, Bicycle Spaces and Mahler Measure
, 2014
"... The space C of conservative vertex colorings (over a field F) of a countably locallyfinite graph G is introduced. The subspace C0 of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Zdaction by automorphisms, C is a finitely generated module ove ..."
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The space C of conservative vertex colorings (over a field F) of a countably locallyfinite graph G is introduced. The subspace C0 of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Zdaction by automorphisms, C is a finitely generated module
A Tutte Polynomial for Coloured Graphs
, 1999
"... We define a polynomial W on graphs with colours on the edges, by generalizing the spanning tree expansion of the Tutte polynomial as far as possible: we give necessary and sufficient conditions on the edge weights for this expansion not to depend on the order used. We give a contractiondeletion for ..."
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We define a polynomial W on graphs with colours on the edges, by generalizing the spanning tree expansion of the Tutte polynomial as far as possible: we give necessary and sufficient conditions on the edge weights for this expansion not to depend on the order used. We give a contraction
Preprocessing Subgraph and Minor Problems: When Does a Small Vertex Cover Help?
, 2014
"... We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph. We provide three sets of simple general conditions characterizing problems admitting kernels of polynomial size. Our characterizations not only give generic explanatio ..."
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explanations for the existence of many known polynomial kernels for problems like qColoring, Odd Cycle Transversal, Chordal Deletion, ηTransversal, or Long Path, parameterized by the size of a vertex cover, but also imply new polynomial kernels for problems like FMinorFree Deletion, which is to delete
Linear Time Parameterized Algorithms for Subset Feedback Vertex Set
"... In the Subset Feedback Vertex Set (Subset FVS) problem, the input is a graph G on n vertices and m edges, a subset of vertices T, referred to as terminals, and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every cycle that contains a termin ..."
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In the Subset Feedback Vertex Set (Subset FVS) problem, the input is a graph G on n vertices and m edges, a subset of vertices T, referred to as terminals, and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every cycle that contains a
List Hcoloring a graph by removing few vertices
"... Abstract. In the deletion version of the list homomorphism problem, we are given graphs G and H, a list L(v) ⊆ V (H) for each vertex v ∈ V (G), and an integer k. The task is to decide whether there exists a set W ⊆ V (G) of size at most k such that there is a homomorphism from G \W to H respecting ..."
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the lists. We show that DLHom(H), parameterized by k and H, is fixedparameter tractable for any (P6, C6)free bipartite graph H; already for this restricted class of graphs, the problem generalizes Vertex Cover, Odd Cycle Transversal, and Vertex Multiway Cut parameterized by the size of the cutset
PlanarF Deletion: Approximation and Optimal FPT Algorithms
"... Let F be a finite set of graphs. In the FDeletion problem, we are given an nvertex, medge graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F as a minor. FDeletion is a generic problem and by ..."
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and by selecting different sets of forbidden minors F, one can obtain various fundamental problems such as Vertex Cover, Feedback Vertex Set or Treewidth ηDeletion. In this paper we obtain a number of generic algorithmic results about FDeletion, when F contains at least one planar graph. The highlights of our
DIRECTED GRAPHS: FIXEDPARAMETER TRACTABILITY & BEYOND
, 2014
"... Most interesting optimization problems on graphs are NPhard, implying that (unless P = NP) there is no polynomial time algorithm that solves all the instances of an NPhard problem exactly. However, classical complexity measures the running time as a function of only the overall input size. The pa ..."
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Most interesting optimization problems on graphs are NPhard, implying that (unless P = NP) there is no polynomial time algorithm that solves all the instances of an NPhard problem exactly. However, classical complexity measures the running time as a function of only the overall input size
Results 1  10
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923