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Non-planarity of Markoff graphs mod p

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On the Dihedral Main Conjectures of Iwasawa Theory for Hilbert Modular Eigenforms

Jeanine Marie Van Order

We construct a bipartite Euler system in the sense of Howard for Hilbert modular eigenforms of parallel weight two over totally real fields, generalizing works of Bertolini-Darmon, Longo, Nekovar, Pollack-Weston, and others. The construction has direct app ...

Canadian Mathematical Soc2013

Lower bounds on the obstacle number of graphs

János Pach, Doemoetoer Palvoelgyi, Padmini Mukkamala

Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be con ...

2012

Wavelet Frames On Graphs Defined By Fmri Functional Connectivity

Dimitri Nestor Alice Van De Ville, Nora Leonardi

Multiscale representations such as the wavelet transform are useful for many signal processing tasks. Graphs are flexible models to represent complex networks and a spectral graph wavelet transform (SGWT) has recently been developed as a generalization of ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Algebraic Algorithms for Vector Network Coding

Christina Fragouli, Javad Ebrahimi Boroojeni

We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying th ...

Institute of Electrical and Electronics Engineers2011

Graphs that Admit Right Angle Crossing Drawings

Radoslav Fulek, Balázs Keszegh, Filip Moric

We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends pe ...

2010

Algebraic techniques for deterministic networks

Christina Fragouli, Javad Ebrahimi Boroojeni

We here summarize some recent advances in the study of linear deterministic networks, recently proposed as approximations for wireless channels. This work started by extending the algebraic framework developed for multicasting over graphs in [1] to include ...

2010

Oriented paths in n-chromatic digraphs

Rajai Nasser

In this thesis, we try to treat the problem of oriented paths in n-chromatic digraphs. We first treat the case of antidirected paths in 5-chromatic digraphs, where we explain El-Sahili’s theorem and provide an elementary and shorter proof of it. We then tr ...

2010

Hypergraphic LP Relaxations for Steiner Trees

David Pritchard

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this ...

Springer2010

Blockers and transversals

Dominique de Werra, Bernard Ries, Rico Zenklusen

Given an undirected graph G = (V, E) with matching number v(G), we define d-blockers as subsets of edges B such that nu((V, E \ B)) = d. ...

2009

Feedback topology and XOR-dynamics in Boolean networks with varying input structure

Carlo Maffi

We analyze a model of fixed in-degree random Boolean networks in which the fraction of input-receiving nodes is controlled by the parameter gamma. We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This ...

2009