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In this paper, we study two graph convexity parameters: iteration time and general position number. The iteration time was defined in 1981 in the geodesic convexity, but its computational complexity was so far open. The general position number was de
Externí odkaz:
http://arxiv.org/abs/2305.00467
Autor:
Protti, Fábio, Thompson, João V. C.
Let $\P$ be any collection of paths of a graph $G=(V,E)$. For $S\subseteq V$, define $I(S)=S\cup\{v\mid v \ \mbox{lies in a path of} \ \P \ \mbox{with endpoints in} \ S\}$. Let $\C$ be the collection of fixed points of the function $I$, that is, $\C=
Externí odkaz:
http://arxiv.org/abs/2303.18029
A walk $u_0u_1 \ldots u_{k-1}u_k$ of a graph $G$ is a \textit{weakly toll walk} if $u_0u_k \not\in E(G)$, $u_0u_i \in E(G)$ implies $u_i = u_1$, and $u_ju_k\in E(G)$ implies $u_j=u_{k-1}$. The {\em weakly toll interval} of a set $S \subseteq V(G)$, d
Externí odkaz:
http://arxiv.org/abs/2303.07414
Publikováno v:
In Discrete Applied Mathematics 15 January 2025 360:246-257
Autor:
Frederiksen, Jette Lautrup a, Massacesi, Luca b, Nielsen, Helle Hvilsted c, Rini, Augusto d, Baldi, Eleonora e, Mirabella, Massimiliano f, Antonella, Falzone Francesca Maria g, Lus, Giacomo h, Paolicelli, Damiano i, Kant, Matthias j, Salemi, Giuseppe k, Aguglia, Umberto l, w, Comi, Cristoforo m, De Riz, Milena n, Barcella, Valeria o, Flemmen, Heidi Ø. p, Protti, Alessandra q, Farbu, Elisabeth r, u, van Exel, Job s, t, Torkildsen, Øivind u, v, ⁎
Publikováno v:
In Multiple Sclerosis and Related Disorders January 2025 93
Publikováno v:
In Applied Mathematics and Computation 15 February 2025 487
Autor:
Protti, Alessandro, Madotto, Fabiana, Florio, Gaetano, Bove, Tiziana, Carlesso, Eleonora, Casella, Giampaolo, Dalla Corte, Francesca, Foti, Giuseppe, Giudici, Riccardo, Langer, Thomas, Montalto, Carlo, Rezoagli, Emanuele, Santini, Alessandro, Terragni, Pierpaolo, Zanella, Alberto, Grasselli, Giacomo, Cecconi, Maurizio
Publikováno v:
In Journal of Critical Care February 2025 85
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 26:2, Graph Theory (April 18, 2024) dmtcs:9837
A walk $u_0u_1 \ldots u_{k-1}u_k$ is a \textit{weakly toll walk} if $u_0u_i \in E(G)$ implies $u_i = u_1$ and $u_ju_k\in E(G)$ implies $u_j=u_{k-1}$. A set $S$ of vertices of $G$ is {\it weakly toll convex} if for any two non-adjacent vertices $x,y \
Externí odkaz:
http://arxiv.org/abs/2203.17056
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey results on chara
Externí odkaz:
http://arxiv.org/abs/2203.15878
Graph convexity spaces have been studied in many contexts. In particular, some studies are devoted to determine if a graph equipped with a convexity space is a {\em convex geometry}. It is well known that chordal and Ptolemaic graphs can be character
Externí odkaz:
http://arxiv.org/abs/2203.05588