The following two conjectures arose in the work of Grimmett and Winkler, and Pemantle: the uniformly random forest F and the uniformly random connected subgraph C of a finite graph G have the edge-negative-association property. In other words, for all distinct edges e and f of G, the probability that F (respectively, C) contains e conditioned on containing f is less than or equal to the probability that F (respectively, C) contains e. Grimmett and Winkler showed that the first conjecture is true for all simple graphs on 8 vertices and all graphs on 9 vertices with at most 18 edges. In this paper, we describe an infinite, nontrivial class of graphs and matroids for which a generalized version of both conjectures holds
This thesis is primarily concerned with correlation inequalities between the number of homomorphic ...
Abstract We discuss various stochastic models (random walk, percolation, the Ising and random-cluste...
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A class of graphs is bridge-addable if given a graph G in the class, any graph obtained by adding an...
This thesis is primarily concerned with correlation inequalities between the number of homomorphic ...
Abstract We discuss various stochastic models (random walk, percolation, the Ising and random-cluste...
In this thesis we consider models of random graphs where, unlike in the classical models G (n, p) t...
Abstract. Consider a randomly oriented graph G = (V, E) and let a, s and b be three distinct vertice...
Abstract. We study random graphs, both G(n, p) and G(n,m), with random orien-tations on the edges. F...
We present a Gaussian random walk in a polytope that starts at a point inside and continues until it...
An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if...
We study the random graph G (n,p) with a random orientation. For three fixed vertices s, a, b in G(n...
A non-empty class A of labelled graphs that is closed under isomorphism is weakly addable if for eac...
This thesis is inspired by the observation that we have no good random model for matroids. That stan...
Abstract. Mason's Conjecture asserts that for an m-element rank r matroid M the sequence Ik=
A collection of graphs is called bridge-alterable if, for each graph G with a bridge e, G is in the ...
We study bipartite subgraphs of a random cubic graph in the thesis. We show, that an edge-maximum bi...
The bases-exchange graph of a matroid is the graph whose vertices are the bases of the matroid, and ...
A class of graphs is bridge-addable if given a graph G in the class, any graph obtained by adding an...
This thesis is primarily concerned with correlation inequalities between the number of homomorphic ...
Abstract We discuss various stochastic models (random walk, percolation, the Ising and random-cluste...
In this thesis we consider models of random graphs where, unlike in the classical models G (n, p) t...
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