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pro vyhledávání: '"P Tuite"'
The general position problem in graph theory asks for the number of vertices in a largest set $S$ of vertices of a graph $G$ such that no shortest path of $G$ contains more than two vertices of $S$. The analogous monophonic position problem is obtain
Externí odkaz:
http://arxiv.org/abs/2412.09837
We consider real linear transformations between two inertial frames with constant relative speed $v$ in a $d$-dimensional spacetime where light moves with constant speed $c=1$ (for some chosen units) in all frames. For $d=2$ we show that the standard
Externí odkaz:
http://arxiv.org/abs/2410.22025
In this paper we consider a colouring version of the general position problem. The \emph{$\gp $-chromatic number} is the smallest number of colours needed to colour $V(G)$ such that each colour class has the no-three-in-line property. We determine bo
Externí odkaz:
http://arxiv.org/abs/2408.13494
A subset $S$ of vertices of a graph $G$ is in \emph{general position} if no shortest path in $G$ contains three vertices of $S$. The \emph{general position problem} consists of finding the number of vertices in a largest general position set of $G$,
Externí odkaz:
http://arxiv.org/abs/2404.19451
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs, in terms
Externí odkaz:
http://arxiv.org/abs/2403.18943
Autor:
Salek, M Sabbir, Thakur, Mugdha Basu, Ala, Pardha Sai Krishna, Chowdhury, Mashrur, Schmid, Matthias, Murray-Tuite, Pamela, Khan, Sakib Mahmud, Krovi, Venkat
Automated vehicle (AV) platooning has the potential to improve the safety, operational, and energy efficiency of surface transportation systems by limiting or eliminating human involvement in the driving tasks. The theoretical validity of the AV plat
Externí odkaz:
http://arxiv.org/abs/2403.05415
A subset of vertices of a graph $G$ is a general position set if no triple of vertices from the set lie on a common shortest path in $G$. In this paper we introduce the general position polynomial as $\sum_{i \geq 0} a_i x^i$, where $a_i$ is the numb
Externí odkaz:
http://arxiv.org/abs/2401.05696
Autor:
Tuite, Michael P., Welby, Michael
We describe Zhu recursion for a vertex operator algebra (VOA) and its modules on a genus $g$ Riemann surface in the Schottky uniformisation. We show that $n$-point (intertwiner) correlation functions are written as linear combinations of $(n-1)$-poin
Externí odkaz:
http://arxiv.org/abs/2312.13717
This paper considers a game version of the general position problem in which a general position set is built through adversarial play. Two players in a graph, Builder and Blocker, take it in turns to add a vertex to a set, such that the vertices of t
Externí odkaz:
http://arxiv.org/abs/2310.19949
Autor:
Mariah Kenney, Iaroslavna Vasylieva, Greg Hood, Ivan Cao-Berg, Luke Tuite, Rozita Laghaei, Megan C. Smith, Alan M. Watson, Alexander J. Ropelewski
Publikováno v:
Scientific Data, Vol 11, Iss 1, Pp 1-11 (2024)
Abstract Advancements in microscopy techniques and computing technologies have enabled researchers to digitally reconstruct brains at micron scale. As a result, community efforts like the BRAIN Initiative Cell Census Network (BICCN) have generated th
Externí odkaz:
https://doaj.org/article/35296c1a2825486db21d5e6865fb98e8
