Concept

Lattice graph

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On the Rainbow Turan number of paths

Abhishek Methuku

Let F be a fixed graph. The rainbow Turan number of F is defined as the maximum number of edges in a graph on n vertices that has a proper edge-coloring with no rainbow copy of F (i.e., a copy of F all of whose edges have different colours). The systematic ...

ELECTRONIC JOURNAL OF COMBINATORICS2019

Learning Graphs From Data: A Signal Representation Perspective

Pascal Frossard, Xiaowen Dong

The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis, and visualization of structured data. When a natural choice of the graph is not readily available from the data sets, it is thus des ...

2019

Approximating the rectilinear crossing number

János Pach

A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph G, (cr) over bar (G), is the mi ...

2019

Graph-based image representation learning

Renata Khasanova

Though deep learning (DL) algorithms are very powerful for image processing tasks, they generally require a lot of data to reach their full potential. Furthermore, there is no straightforward way to impose various properties, given by the prior knowledge a ...

EPFL2019

A Regularization Framework for Learning Over Multitask Graphs

Ali H. Sayed, Stefan Vlaski, Roula Nassif

This letter proposes a general regularization framework for inference over multitask networks. The optimization approach relies on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term that allows to incorporate ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Slepian Guided Filtering of Graph Signals

Dimitri Nestor Alice Van De Ville, Miljan Petrovic

Joint localization of graph signals in vertex and spectral domain is achieved in Slepian vectors calculated by either maximizing energy concentration (mu) or minimizing modified embedded distance (xi) in the subgraph of interest. On the other hand, graph L ...

SPIE-INT SOC OPTICAL ENGINEERING2019

Efficient large-scale graph processing: optimisations for storage, performance and evolving graphs

Jasmina Malicevic

Graph processing systems are used in a wide variety of fields, ranging from biology to social networks. Algorithms to mine graphs incur many random accesses, and the sparse nature of the graphs of interest, exacerbates this. As DRAM sustains high bandwidt ...

EPFL2019

Graph Reduction with Spectral and Cut Guarantees

Andreas Loukas

Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity measure used for g ...

MICROTOME PUBL2019

Stability results for vertex Turatn problems in Kneser graphs

Abhishek Methuku

The vertex set of the Kneser graph K(n, k) is V = (([n])(k)) and two vertices are adjacent if the corresponding sets are disjoint. For any graph F, the largest size of a vertex set U subset of V such that K(n, k)[U] is F-free, was recently determined by Al ...

ELECTRONIC JOURNAL OF COMBINATORICS2019

Generalized Turan Problems For Even Cycles

Abhishek Methuku

Given a graph H and a set of graphs F, let ex(n, H, F) denote the maximum possible number of copies of H in an T-free graph on n vertices. We investigate the function ex(n, H, F), when H and members of F are cycles. Let C-k denote the cycle of length k and ...

2019