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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
Autor:
Thankachy, Maya, Thomas, Elias John, Chandran, Ullas, Tuite, James, Di Stefano, Gabriele, Erskine, Grahame
In this paper we generalise the notion of visibility from a point in an integer lattice to the setting of graph theory. For a vertex $x$ of a connected graph $G$, we say that a set $S \subseteq V(G)$ is an \emph{$x$-position set} if for any $y \in S$
Externí odkaz:
http://arxiv.org/abs/2209.00359
The general position problem for graphs was inspired by the no-three-in-line problem from discrete geometry. A set $S$ of vertices of a graph $G$ is a \emph{general position set} if no shortest path in $G$ contains three or more vertices of $S$. The
Externí odkaz:
http://arxiv.org/abs/2203.08170
Publikováno v:
In Discrete Applied Mathematics 15 September 2024 354:72-82
Publikováno v:
In Discrete Applied Mathematics 15 August 2024 353:29-43
Autor:
Stephens, Gareth F., Wilson, Jack A., Curling, Simon F., He, Guanze, Thomas, P. John, Williams, David W., Ortner, Susan, Grovenor, Chris, Rushton, Michael J.D., Baker, Aidan Cole, Middleburgh, Simon C.
Publikováno v:
In Progress in Nuclear Energy June 2024 171
The general position number of a graph $G$ is the size of the largest set of vertices $S$ such that no geodesic of $G$ contains more than two elements of $S$. The monophonic position number of a graph is defined similarly, but with `induced path' in
Externí odkaz:
http://arxiv.org/abs/2106.06827
The general position problem in graph theory asks for the largest set $S$ of vertices of a graph $G$ such that no shortest path of $G$ contains more than two vertices of $S$. In this paper we consider a variant of the general position problem called
Externí odkaz:
http://arxiv.org/abs/2012.10330
Getting inspired by the famous no-three-in-line problem and by the general position subset selection problem from discrete geometry, the same is introduced into graph theory as follows. A set $S$ of vertices in a graph $G$ is a general position set i
Externí odkaz:
http://arxiv.org/abs/2004.04648
Publikováno v:
In Energy Nexus September 2023 11