Zobrazeno 1 - 10
of 1 238
pro vyhledávání: '"P, Foucaud"'
A monitoring edge-geodetic set of a graph is a subset $M$ of its vertices such that for every edge $e$ in the graph, deleting $e$ increases the distance between at least one pair of vertices in $M$. We study the following computational problem \texts
Externí odkaz:
http://arxiv.org/abs/2409.19067
Monitoring edge-geodetic sets in a graph are subsets of vertices such that every edge of the graph must lie on all the shortest paths between two vertices of the monitoring set. These objects were introduced in a work by Foucaud, Krishna and Ramasubr
Externí odkaz:
http://arxiv.org/abs/2409.00350
An identifying open code of a graph $G$ is a set $S$ of vertices that is both a separating open code (that is, $N_G(u) \cap S \ne N_G(v) \cap S$ for all distinct vertices $u$ and $v$ in $G$) and a total dominating set (that is, $N(v) \cap S \ne \empt
Externí odkaz:
http://arxiv.org/abs/2407.09692
Autor:
Foucaud, Florent, Galby, Esther, Khazaliya, Liana, Li, Shaohua, Inerney, Fionn Mc, Sharma, Roohani, Tale, Prafullkumar
For a graph $G$, a subset $S\subseteq V(G)$ is called a resolving set of $G$ if, for any two vertices $u,v\in V(G)$, there exists a vertex $w\in S$ such that $d(w,u)\neq d(w,v)$. The Metric Dimension problem takes as input a graph $G$ on $n$ vertices
Externí odkaz:
http://arxiv.org/abs/2405.01344
An $\textit{identifying code}$ of a closed-twin-free graph $G$ is a set $S$ of vertices of $G$ such that any two vertices in $G$ have a distinct intersection between their closed neighborhood and $S$. It was conjectured that there exists a constant $
Externí odkaz:
http://arxiv.org/abs/2403.17877
An $\textit{identifying code}$ of a closed-twin-free graph $G$ is a dominating set $S$ of vertices of $G$ such that any two vertices in $G$ have a distinct intersection between their closed neighborhoods and $S$. It was conjectured that there exists
Externí odkaz:
http://arxiv.org/abs/2403.13172
Autor:
Foucaud, Florent, Marcille, Pierre-Marie, Myint, Zin Mar, Sandeep, R. B., Sen, Sagnik, Taruni, S.
A monitoring edge-geodetic set, or simply an MEG-set, of a graph $G$ is a vertex subset $M \subseteq V(G)$ such that given any edge $e$ of $G$, $e$ lies on every shortest $u$-$v$ path of $G$, for some $u,v \in M$. The monitoring edge-geodetic number
Externí odkaz:
http://arxiv.org/abs/2403.09122
In this paper, we study a dynamic analogue of the Path Cover problem, which can be solved in polynomial-time in directed acyclic graphs. A temporal digraph has an arc set that changes over discrete time-steps, if the underlying digraph (the union of
Externí odkaz:
http://arxiv.org/abs/2403.04589
We investigate fine-grained algorithmic aspects of identification problems in graphs and set systems, with a focus on Locating-Dominating Set and Test Cover. We prove the (tight) conditional lower bounds for these problems when parameterized by treew
Externí odkaz:
http://arxiv.org/abs/2402.08346
For a graph $ G = (V, E) $ with a vertex set $ V $ and an edge set $ E $, a function $ f : V \rightarrow \{0, 1, 2, . . . , diam(G)\} $ is called a \emph{broadcast} on $ G $. For each vertex $ u \in V $, if there exists a vertex $ v $ in $ G $ (possi
Externí odkaz:
http://arxiv.org/abs/2312.10485