Zobrazeno 1 - 10
of 231
pro vyhledávání: '"DI STEFANO, Gabriele"'
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
Visibility problems have been investigated for a long time under different assumptions as they pose challenging combinatorial problems and are connected to robot navigation problems. The mutual-visibility problem in a graph $G$ of $n$ vertices asks t
Externí odkaz:
http://arxiv.org/abs/2407.00409
For a set of robots (or agents) moving in a graph, two properties are highly desirable: confidentiality (i.e., a message between two agents must not pass through any intermediate agent) and efficiency (i.e., messages are delivered through shortest pa
Externí odkaz:
http://arxiv.org/abs/2405.13615
The mutual-visibility problem in a graph $G$ asks for the cardinality of a largest set of vertices $S\subseteq V(G)$ so that for any two vertices $x,y\in S$ there is a shortest $x,y$-path $P$ so that all internal vertices of $P$ are not in $S$. This
Externí odkaz:
http://arxiv.org/abs/2401.02373
Autor:
Cicerone, Serafino, Di Fonso, Alessia, Di Stefano, Gabriele, Navarra, Alfredo, Piselli, Francesco
Let $G$ be a graph and $X\subseteq V(G)$. Then, vertices $x$ and $y$ of $G$ are $X$-visible if there exists a shortest $u,v$-path where no internal vertices belong to $X$. The set $X$ is a mutual-visibility set of $G$ if every two vertices of $X$ are
Externí odkaz:
http://arxiv.org/abs/2308.14443
The \textsc{Mutual Visibility} is a well-known problem in the context of mobile robots. For a set of $n$ robots disposed in the Euclidean plane, it asks for moving the robots without collisions so as to achieve a placement ensuring that no three robo
Externí odkaz:
http://arxiv.org/abs/2308.01855
The concept of mutual-visibility in graphs has been recently introduced. If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u, v\}$. If
Externí odkaz:
http://arxiv.org/abs/2307.10661
A subset $S$ of vertices of a graph $G$ is a \emph{general position set} if no shortest path in $G$ contains three or more vertices of $S$. In this paper, we generalise a problem of M. Gardner to graph theory by introducing the \emph{lower general po
Externí odkaz:
http://arxiv.org/abs/2306.09965
Autor:
Cicerone, Serafino, Di Stefano, Gabriele, Drozek, Lara, Hedzet, Jaka, Klavzar, Sandi, Yero, Ismael G.
If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u,v\}$. If each two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibilit
Externí odkaz:
http://arxiv.org/abs/2304.00864
Let $G$ be a graph and $X\subseteq V(G)$. Then $X$ is a mutual-visibility set if each pair of vertices from $X$ is connected by a geodesic with no internal vertex in $X$. The mutual-visibility number $\mu(G)$ of $G$ is the cardinality of a largest mu
Externí odkaz:
http://arxiv.org/abs/2210.07835