Zobrazeno 1 - 10
of 115
pro vyhledávání: '"Messinger M"'
We study a discrete-time model for the spread of information in a graph, motivated by the idea that people believe a story when they learn of it from two different origins. Similar to the burning number, in this problem, information spreads in rounds
Externí odkaz:
http://arxiv.org/abs/2411.02050
We introduce a discrete-time immunization version of the SEIS compartment model of infection by a contagious disease, with an extended latency and protective period. The population is modeled by a graph $H$ where vertices represent individuals and ed
Externí odkaz:
http://arxiv.org/abs/2408.05313
This paper considers the Cops and Attacking Robbers game, a variant of Cops and Robbers, where the robber is empowered to attack a cop in the same way a cop can capture the robber. In a graph $G$, the number of cops required to capture a robber in th
Externí odkaz:
http://arxiv.org/abs/2408.02225
Autor:
Messinger, M. E., Porter, A.
For a graph $G$, the vertices of the $k$-dominating graph, denoted $\mathcal{D}_k(G)$, correspond to the dominating sets of $G$ with cardinality at most $k$. Two vertices of $\mathcal{D}_k(G)$ are adjacent if and only if the corresponding dominating
Externí odkaz:
http://arxiv.org/abs/2404.10962
Eternal domination is a dynamic process by which a graph is protected from an infinite sequence of vertex intrusions. In eternal distance-$k$ domination, guards initially occupy the vertices of a distance-$k$ dominating set. After a vertex is attacke
Externí odkaz:
http://arxiv.org/abs/2104.03835
We introduce a new variant of the game of Cops and Robbers played on graphs, where the robber is invisible unless outside the neighbor set of a cop. The hyperopic cop number is the corresponding analogue of the cop number, and we investigate bounds a
Externí odkaz:
http://arxiv.org/abs/1710.10112
We consider a variation of the Cops and Robber game where the cops can only see the robber when the distance between them is at most a fixed parameter $\ell$. We consider the basic consequences of this definition for some simple graph families, and s
Externí odkaz:
http://arxiv.org/abs/1708.07179
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol. 20 no. 1, Graph Theory (January 17, 2018) dmtcs:2039
We introduce a natural variant of the parallel chip-firing game, called the diffusion game. Chips are initially assigned to vertices of a graph. At every step, all vertices simultaneously send one chip to each neighbour with fewer chips. As the dynam
Externí odkaz:
http://arxiv.org/abs/1609.05792
In this paper, we provide results for the search number of the Cartesian product of graphs. We consider graphs on opposing ends of the spectrum: paths and cliques. Our main result determines the pathwidth of the product of cliques and provides a lowe
Externí odkaz:
http://arxiv.org/abs/1604.04509
In this short note, we supply a new upper bound on the cop number in terms of tree decompositions. Our results in some cases extend a previously derived bound on the cop number using treewidth.
Externí odkaz:
http://arxiv.org/abs/1308.2839