862 research outputs found

    Independent Sets in Graphs with an Excluded Clique Minor

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    Let GG be a graph with nn vertices, with independence number α\alpha, and with with no Kt+1K_{t+1}-minor for some t5t\geq5. It is proved that (2α1)(2t5)2n5(2\alpha-1)(2t-5)\geq2n-5

    STABILIZATION POLICIES AND AGRICULTURAL IMPACTS IN DEVELOPING COUNTRIES: THE CASE OF BOLIVIA

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    This research examines the success of stabilization policies to control hyperinflation in Bolivia. Money demand functions for the hyperinflation and stabilization periods were econometrically estimated and statistically tested. We conclude that the demand for money in Bolivia changed after stabilization policies were implemented, indicating that the new government's objectives were met. Stabilization policies resulted in real economic growth for Bolivia's economy, including its agricultural sector, where agricultural export shares increased tenfold as stabilization policies corrected overvalued exchange rates.Bolivia, Developing countries, Hyperinflation, Money demand, Stabilization policies, Political Economy,

    A Note on Hadwiger's Conjecture

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    Hadwiger's Conjecture states that every Kt+1K_{t+1}-minor-free graph is tt-colourable. It is widely considered to be one of the most important conjectures in graph theory. If every Kt+1K_{t+1}-minor-free graph has minimum degree at most δ\delta, then every Kt+1K_{t+1}-minor-free graph is (δ+1)(\delta+1)-colourable by a minimum-degree-greedy algorithm. The purpose of this note is to prove a slightly better upper bound

    Grad and classes with bounded expansion I. decompositions

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    We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r, grad r(G). For these classes we prove the existence of several partition results such as the existence of low tree-width and low tree-depth colorings. This generalizes and simplifies several earlier results (obtained for minor closed classes)

    Connected matchings in special families of graphs.

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    A connected matching in a graph is a set of disjoint edges such that, for any pair of these edges, there is another edge of the graph incident to both of them. This dissertation investigates two problems related to finding large connected matchings in graphs. The first problem is motivated by a famous and still open conjecture made by Hadwiger stating that every k-chromatic graph contains a minor of the complete graph Kk . If true, Hadwiger\u27s conjecture would imply that every graph G has a minor of the complete graph K n/a(C), where a(G) denotes the independence number of G. For a graph G with a(G) = 2, Thomassé first noted the connection between connected matchings and large complete graph minors: there exists an ? \u3e 0 such that every graph G with a( G) = 2 contains K ?+, as a minor if and only if there exists a positive constant c such that every graph G with a( G) = 2 contains a connected matching of size cn. In Chapter 3 we prove several structural properties of a vertexminimal counterexample to these statements, extending work by Blasiak. We also prove the existence of large connected matchings in graphs with clique size close to the Ramsey bound by proving: for any positive constants band c with c \u3c ¼, there exists a positive integer N such that, if G is a graph with n =: N vertices, 0\u27( G) = 2, and clique size at most bv(n log(n) )then G contains a connected matching of size cn. The second problem concerns computational complexity of finding the size of a maximum connected matching in a graph. This problem has many applications including, when the underlying graph is chordal bipartite, applications to the bipartite margin shop problem. For general graphs, this problem is NP-complete. Cameron has shown the problem is polynomial-time solvable for chordal graphs. Inspired by this and applications to the margin shop problem, in Chapter 4 we focus on the class of chordal bipartite graphs and one of its subclasses, the convex bipartite graphs. We show that a polynomial-time algorithm to find the size of a maximum connected matching in a chordal bipartite graph reduces to finding a polynomial-time algorithm to recognize chordal bipartite graphs that have a perfect connected matching. We also prove that, in chordal bipartite graphs, a connected matching of size k is equivalent to several other statements about the graph and its biadjacency matrix, including for example, the statement that the complement of the latter contains a k x k submatrix that is permutation equivalent to strictly upper triangular matrix

    Emergent behavior of soil fungal dynamics:influence of soil architecture and water distribution

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    Macroscopic measurements and observations in two-dimensional soil-thin sections indicate that fungal hyphae invade preferentially the larger, air-filled pores in soils. This suggests that the architecture of soils and the microscale distribution of water are likely to influence significantly the dynamics of fungal growth. Unfortunately, techniques are lacking at present to verify this hypothesis experimentally, and as a result, factors that control fungal growth in soils remain poorly understood. Nevertheless, to design appropriate experiments later on, it is useful to indirectly obtain estimates of the effects involved. Such estimates can be obtained via simulation, based on detailed micron-scale X-ray computed tomography information about the soil pore geometry. In this context, this article reports on a series of simulations resulting from the combination of an individual-based fungal growth model, describing in detail the physiological processes involved in fungal growth, and of a Lattice Boltzmann model used to predict the distribution of air-liquid interfaces in soils. Three soil samples with contrasting properties were used as test cases. Several quantitative parameters, including Minkowski functionals, were used to characterize the geometry of pores, air-water interfaces, and fungal hyphae. Simulation results show that the water distribution in the soils is affected more by the pore size distribution than by the porosity of the soils. The presence of water decreased the colonization efficiency of the fungi, as evinced by a decline in the magnitude of all fungal biomass functional measures, in all three samples. The architecture of the soils and water distribution had an effect on the general morphology of the hyphal network, with a "looped" configuration in one soil, due to growing around water droplets. These morphologic differences are satisfactorily discriminated by the Minkowski functionals, applied to the fungal biomass
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