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Random procedures for dominating sets in bipartite graphs

Sarah Artmann, Jochen Harant (2010)

Discussiones Mathematicae Graph Theory

Using multilinear functions and random procedures, new upper bounds on the domination number of a bipartite graph in terms of the cardinalities and the minimum degrees of the two colour classes are established.

Random threshold graphs.

Reilly, Elizabeth Perez, Scheinerman, Edward R. (2009)

The Electronic Journal of Combinatorics [electronic only]

Random walk on a building of type Ãr and brownian motion of the Weyl chamber

Bruno Schapira (2009)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we study a random walk on an affine building of type Ãr, whose radial part, when suitably normalized, converges toward the brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to the one of Biane (Probab. Theory Related Fields89 (1991) 117–129). This extends also the link at the probabilistic level between riemannian symmetric spaces of the noncompact type and their discrete counterpart, which had been previously discovered by Bougerol...

Random walks on the affine group of local fields and of homogeneous trees

Donald I. Cartwright, Vadim A. Kaimanovich, Wolfgang Woess (1994)

Annales de l'institut Fourier

The affine group of a local field acts on the tree 𝕋 ( 𝔉 ) (the Bruhat-Tits building of GL ( 2 , 𝔉 ) ) with a fixed point in the space of ends 𝕋 ( F ) . More generally, we define the affine group Aff ( 𝔉 ) of any homogeneous tree 𝕋 as the group of all automorphisms of 𝕋 with a common fixed point in 𝕋 , and establish main asymptotic properties of random products in Aff ( 𝔉 ) : (1) law of large numbers and central limit theorem; (2) convergence to 𝕋 and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...

Randomly H graphs

Gary Chartrand, Ortrud R. Oellermann, Sergio Ruiz (1986)

Mathematica Slovaca

Rank decomposition in zero pattern matrix algebras

Harm Bart, Torsten Ehrhardt, Bernd Silbermann (2016)

Czechoslovak Mathematical Journal

For a block upper triangular matrix, a necessary and sufficient condition has been given to let it be the sum of block upper rectangular matrices satisfying certain rank constraints; see H. Bart, A. P. M. Wagelmans (2000). The proof involves elements from integer programming and employs Farkas' lemma. The algebra of block upper triangular matrices can be viewed as a matrix algebra determined by a pattern of zeros. The present note is concerned with the question whether the decomposition result referred...

Rank numbers for bent ladders

Peter Richter, Emily Leven, Anh Tran, Bryan Ek, Jobby Jacob, Darren A. Narayan (2014)

Discussiones Mathematicae Graph Theory

A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices with the same label contains a vertex with a larger label. The rank number of a graph is the fewest number of labels that can be used in a ranking. The rank number of a graph is known for many families, including the ladder graph P2 × Pn. We consider how ”bending” a ladder affects the rank number. We prove that in certain cases the rank number does not change, and in others the rank...

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