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pro vyhledávání: '"Elias, John"'
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:
Elias John Elenjickal, Anna T. Valson, Santosh Varughese, Lloyd Vincent, Edwin Fernando, Gopalakrishnan Natarajan
Publikováno v:
Frontiers in Pharmacology, Vol 15 (2024)
Externí odkaz:
https://doaj.org/article/56541738a3cb429ca38f0c21d5bbe74e
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
Publikováno v:
In Journal of ISAKOS December 2024 9(6)
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
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
Autor:
Melvin, Patricia R., Wheatley, Benjamin M., Schimoler, Patrick J., Kharlamov, Alexander, Miller, Mark C., Elias, John J., Altman, Gregory T.
Publikováno v:
In Journal of Biomechanics March 2024 165