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

Publications associées (32)

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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

Principal Patterns on Graphs: Discovering Coherent Structures in Datasets

Pierre Vandergheynst, Kirell Maël Benzi, Benjamin Ricaud

Graphs are now ubiquitous in almost every field of research. Recently, new research areas devoted to the analysis of graphs and data associated to their vertices have emerged. Focusing on dynamical processes, we propose a fast, robust and scalable framewor ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Independence number of generalized Petersen graphs

Javad Ebrahimi Boroojeni

Determining the size of a maximum independent set of a graph G, denoted by alpha(G), is an NP-hard problem. Therefore many attempts are made to find upper and lower bounds, or exact values of alpha(G) for special classes of graphs. This paper is aimed towa ...

Charles Babbage Res Ctr2016

Clustered planarity testing revisited

Radoslav Fulek, Jan Kyncl, Igor Malinovic

The Hanani--Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generali ...

2015

Approximations for Stochastic Graph Rewriting

Sandro Stucki

In this note we present a method to compute approximate descriptions of a class of stochastic systems. For the method to apply, the system must be presented as a Markov chain on a state space consisting in graphs or graph-like objects, and jumps must be de ...

Springer International Publishing2014

The simplicity of planar networks

Emanuele Strano, Marc Barthélemy

Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and ...

Nature Publishing Group2013

THE NUMBER OF EDGES IN k-QUASI-PLANAR GRAPHS

János Pach

A graph drawn in the plane is called k-quasi-planar if it does not contain k pair-wise crossing edges. It has been conjectured for a long time that for every fixed k, the maximum number of edges of a k-quasi-planar graph with n vertices is O(n). The best k ...

Siam Publications2013

A Bayesian Method for Matching Two Similar Graphs without Seeds

Matthias Grossglauser, Pedram Pedarsani

Approximate graph matching (AGM) refers to the problem of mapping the vertices of two structurally similar graphs, which has applications in social networks, computer vision, chemistry, and biology. Given its computational cost, AGM has mostly been limited ...

2013

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

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