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A Precise Threshold For Quasi-Ramsey Numbers

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Vertex-Frequency Analysis on Graphs

Pierre Vandergheynst, Benjamin Ricaud, David Shuman

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric structure of the ...

Academic Press Inc Elsevier Science2016

On the Zarankiewicz problem for intersection hypergraphs

János Pach

Let d and t be fixed positive integers, and let denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem ...

Academic Press Inc Elsevier Science2016

Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames

Pierre Vandergheynst, David Shuman

We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph wavelet constructions ...

Institute of Electrical and Electronics Engineers2015

Heuristic-driven Graph Wavelet Modeling of Complex Terrain

Alexandre Buttler, François Golay, Alexander Ludwig Johannes Peringer, Ioana Stoicescu

We present a novel method for building a multiresolution representation of large digital surface models. The surface points coincide with the nodes of a planar graph which can be processed using a critically sampled, invertible lifting scheme. To drive the ...

Spie-Int Soc Optical Engineering2015

When Can Two Unlabeled Networks Be Aligned Under Partial Overlap?

Matthias Grossglauser, Ehsan Kazemi, Lyudmila Yartseva

Network alignment refers to the problem of matching the vertex sets of two unlabeled graphs, which can be viewed as a generalization of the classic graph isomorphism problem. Network alignment has applications in several fields, including social network an ...

2015

Homometric sets in trees

Radoslav Fulek, Slobodan Mitrovic

Let G = (V, E) denote a simple graph with vertex set V and edge set E. The profile of a vertex set V' subset of V denotes the multiset of pairwise distances between the vertices of V'. Two disjoint subsets of V are homometric if their profiles are the same ...

Academic Press Ltd- Elsevier Science Ltd2014

Diameter Graphs in R-4

Andrei Kupavskii

A diameter graph in is a graph whose set of vertices is a finite subset of and whose set of edges is formed by pairs of vertices that are at diameter apart. This paper is devoted to the study of different extremal properties of diameter graphs in and on a ...

Springer2014

Exploring the Volumetric City. A Methodology for Investigating the Topology and Morphology of Surface and Subsurface Urban Spatial Networks

Michael Robert Doyle

The urban underground has historically been developed as a series of sporadic responses to surface land shortage or to hide unsightly urban activities (Parriaux et al 2004; 2010). The Deep City project at the École polytechnique fédérale de Lausanne in Swi ...

2014

Using Pareto optimality to explore the topology and dynamics of the human connectome

Jean-Philippe Thiran, Alessandra Griffa, Patric Hagmann, Olaf Sporns

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resu ...

Royal Soc2014

Bootstrap Percolation in Power-Law Random Graphs

Léo Hamed Amini

A bootstrap percolation process on a graph is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least infected neighbours becomes infected and remai ...

Springer2014