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Minimum Spanning Trees for MinorClosed Graph Classes in Parallel
, 1997
"... For each minorclosed graph class we show that a simple variant of Boruvka's algorithm computes a MST for any input graph belonging to that class with linear costs. Among minorclosed graph classes are e.g planar graphs, graphs of bounded genus, partial ktrees for fixed k, and linkless or knot ..."
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For each minorclosed graph class we show that a simple variant of Boruvka's algorithm computes a MST for any input graph belonging to that class with linear costs. Among minorclosed graph classes are e.g planar graphs, graphs of bounded genus, partial ktrees for fixed k, and linkless
The Complexity of Learning Minor Closed Graph Classes
, 1995
"... The paper considers the problem of learning classes of graphs closed under taking minors. It is shown that any such class can be properly learned in polynomial time using membership and equivalence queries. The representation of the class is in terms of a set of minimal excluded minors (obstruction ..."
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The paper considers the problem of learning classes of graphs closed under taking minors. It is shown that any such class can be properly learned in polynomial time using membership and equivalence queries. The representation of the class is in terms of a set of minimal excluded minors (obstruction
Strengthening Erdős–Pósa property for minorclosed graph classes
 JOURNAL OF GRAPH THEORY, 66(3):235–240, 2011
, 2011
"... Let H and G be graph classes. We say that H has the Erd”os–Pósa property for G if for any graph G∈G, the minimum vertex covering of all Hsubgraphs of G is bounded by a function f of the maximum packing of Hsubgraphs in G (by Hsubgraph of G we mean any subgraph of G that belongs to H). Robertso ..."
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Let H and G be graph classes. We say that H has the Erd”os–Pósa property for G if for any graph G∈G, the minimum vertex covering of all Hsubgraphs of G is bounded by a function f of the maximum packing of Hsubgraphs in G (by Hsubgraph of G we mean any subgraph of G that belongs to H
Two Linear Time Algorithms for MST on Minor Closed Graph Classes
, 2002
"... This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(V + E) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge of the structure of th ..."
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This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(V + E) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge of the structure
Two Linear Time Algorithms for MST on Minor Closed Graph Classes
"... Abstract: This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(jV j + jEj) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge of the struct ..."
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Abstract: This article presents two simple deterministic algorithms for finding the Minimum Spanning Tree in O(jV j + jEj) time for any proper class of graphs closed on graph minors, which includes planar graphs and graphs of bounded genus. Both algorithms require no a priori knowledge
Handling Proper MinorClosed Graph Classes in Linear Time: Shortest Paths and 2Approximate Steiner Trees
, 2007
"... We generalize the lineartime shortestpaths algorithm for planar graphs with nonnegative edgeweights of Henzinger et al. (1994) to work for any proper class of minorclosed graphs. We show by a counterexample that their algorithm can not be adapted straightforwardly to all proper minorclosed cla ..."
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We generalize the lineartime shortestpaths algorithm for planar graphs with nonnegative edgeweights of Henzinger et al. (1994) to work for any proper class of minorclosed graphs. We show by a counterexample that their algorithm can not be adapted straightforwardly to all proper minorclosed
Model Checking for SuccessorInvariant FirstOrder Logic on MinorClosed Graph Classes
"... Model checking problems for first and monadic secondorder logic on graphs have received considerable attention in the past, not the least due to their connections to problems in algorithmic graph structure theory. While the model checking problem for these logics on general graphs is computationa ..."
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is computationally intractable, it becomes tractable on important classes of graphs such as those of bounded treewidth, planar graphs or more generally, classes of graphs excluding a fixed minor. It is well known that allowing an order relation or successor function can greatly increase the expressive power
Additive Approximation Algorithms for ListColoring MinorClosed Class of Graphs
"... It is known that computing the list chromatic number is harder than computing the chromatic number (assuming NP ̸ = coNP). In fact, the problem of deciding whether a given graph is flistcolorable for a function f: V → {c − 1, c} for c ≥ 3 is Π p 2complete. In general, it is believed that approxim ..."
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that approximating list coloring is hard for dense graphs. In this paper, we are interested in sparse graphs. More specifically, we deal with nontrivial minorclosed classes of graphs, i.e., graphs excluding some Kk minor. We refine the seminal structure theorem of Robertson and Seymour, and then give an additive
Structure in minorclosed classes of matroids
 Surveys in Combinatorics 2013, London Math. Soc. Lecture Notes 409
, 2013
"... This paper gives an informal introduction to structure theory for minorclosed classes of matroids representable over a fixed finite field. The early sections describe some historical results that give evidence that welldefined structure exists for members of such classes. In later sections we desc ..."
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describe the fundamental classes and other features that necessarily appear in structure theory for minorclosed classes of matroids. We conclude with an informal statement of the structure theorem itself. This theorem generalises the Graph Minors Structure Theorem of Robertson and Seymour. 1
Results 1  10
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11,769