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pro vyhledávání: '"Bonichon, Nicolas"'
The Freeze-Tag Problem, introduced in Arkin et al. (SODA'02) consists of waking up a swarm of $n$ robots, starting from a single active robot. In the basic geometric version, every robot is given coordinates in the plane. As soon as a robot is awaken
Externí odkaz:
http://arxiv.org/abs/2402.03258
Autor:
Bonichon, Nicolas, Morel, Pierre-Jean
Publikováno v:
Journal of Integer Sequences, Vol. 25: Article 22.8.3, 2022
A permutation of size $n$ can be identified to its diagram in which there is exactly one point per row and column in the grid $[n]^2$. In this paper we consider multidimensional permutations (or $d$-permutations), which are identified to their diagra
Externí odkaz:
http://arxiv.org/abs/2202.12677
In 1968, Gallai conjectured that the edges of any connected graph with $n$ vertices can be partitioned into $\lceil \frac{n}{2} \rceil$ paths. We show that this conjecture is true for every planar graph. More precisely, we show that every connected p
Externí odkaz:
http://arxiv.org/abs/2110.08870
We present a bijection for toroidal maps that are essentially $3$-connected ($3$-connected in the periodic planar representation). Our construction actually proceeds on certain closely related bipartite toroidal maps with all faces of degree $4$ exce
Externí odkaz:
http://arxiv.org/abs/1907.04016
Autor:
Bonichon, Nicolas, Lévêque, Benjamin
Transversal structures (also known as regular edge labelings) are combinatorial structures defined over 4-connected plane triangulations with quadrangular outer-face. They have been intensively studied and used for many applications (drawing algorith
Externí odkaz:
http://arxiv.org/abs/1707.08191
The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears to be difficult. To approach it, we define and count families of subs
Externí odkaz:
http://arxiv.org/abs/1610.09837
Autor:
Bonichon, Nicolas, Bose, Prosenjit, Carmi, Paz, Kostitsyna, Irina, Lubiw, Anna, Verdonschot, Sander
A geometric graph is angle-monotone if every pair of vertices has a path between them that---after some rotation---is $x$- and $y$-monotone. Angle-monotone graphs are $\sqrt 2$-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmu
Externí odkaz:
http://arxiv.org/abs/1608.08892
Autor:
Bonichon, Nicolas
Quelques algorithmes entre le monde des graphes et les nuages de points.
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00922501
http://tel.archives-ouvertes.fr/docs/00/92/25/01/PDF/hdr.pdf
http://tel.archives-ouvertes.fr/docs/00/92/25/01/PDF/hdr.pdf
Publikováno v:
In European Journal of Combinatorics June 2021 95
Autor:
Bonichon, Nicolas, Bose, Prosenjit, De Carufel, Jean-Lou, Perković, Ljubomir, Van Renssen, André
Consider a weighted graph G where vertices are points in the plane and edges are line segments. The weight of each edge is the Euclidean distance between its two endpoints. A routing algorithm on G has a competitive ratio of c if the length of the pa
Externí odkaz:
http://arxiv.org/abs/1501.01783