Concept

Petersen graph

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Synthesis of Homogeneous Manganese-Doped Titanium Oxide Nanotubes from Titanate Precursors

László Forró, Arnaud Magrez, Kurt Schenk, Endre Horvath, Bálint Náfrádi, Rita Smajda, Péter Szirmai, Zlatko Mickovic

We report a novel synthesis route of homogeneously manganese-doped TiO2 nanotubes in a broad concentration range. The scroll-type trititanate (H2Ti3O7) nanotubes prepared by hydrothermal synthesis were used as precursors. Mn2+ ions were introduced by an io ...

Amer Chemical Soc2013

Tangled Thrackles

János Pach

A tangle is a graph drawn in the plane so that any pair of edges have precisely one point in common, and this point is either an endpoint or a point of tangency. If we allow a third option: the common point may be a proper crossing between the two edges, t ...

Springer Berlin Heidelberg2012

Robust Non-Rigid Registration of 2D and 3D Graphs

Pascal Fua, Jan Kybic, Przemyslaw Rafal Glowacki

We present a new approach to matching graphs embedded in R2 or R3. Unlike earlier methods, our approach does not rely on the similarity of local appearance features, does not require an initial alignment, can handle partial matches, and can cope with non-l ...

2012

Intersection Patterns of Edges in Topological Graphs

Radoslav Fulek

This thesis is devoted to crossing patterns of edges in topological graphs. We consider the following four problems: A thrackle is a graph drawn in the plane such that every pair of edges meet exactly once: either at a common endpoint or in a proper crossi ...

EPFL2012

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

Are motorways rational from slime mould's point of view ?

Emanuele Strano

We analyse the results of our experimental laboratory approximation of motorways networks with slime mould Physarum polycephalum. Motorway networks of fourteen geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, I ...

2012

Graphs That Admit Polyline Drawings with Few Crossing Angles

Radoslav Fulek

We consider graphs that admit polyline drawings where all crossings occur at the same angle alpha is an element of (0, pi/2]. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has O(n) edges. This r ...

2012

Graph Drawing

Radoslav Fulek, Fabrizio Frati

In this paper we study the page number of upward planar directed acyclic graphs. We prove that the page number of any upward planar directed acyclic graph G is a function of the page number of a four-connected subgraph of G; further, we provide an upper bo ...

Springer Berlin Heidelberg2012

Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

Yannick Rochat

By combining evolutionary game theory and graph theory, “games on graphs” study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of uni ...

Public Library of Science2012

Learning of Structured Graph Dictionaries

Pascal Frossard, Xiaowen Dong, Xue Zhang

We propose a method for learning dictionaries towards sparse approximation of signals defined on vertices of arbitrary graphs. Dictionaries are expected to describe effectively the main spatial and spectral components of the signals of interest, so that th ...

2012