The 2-burning number of a graph
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 and a new source can appear in each round. For a...
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Zusammenfassung: | 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 and a new source can appear in each round. For a
graph $G$, we are interested in $b_2(G)$, the minimum number of rounds until
the information has spread to all vertices of graph $G$. We are also interested
in finding $t_2(G)$, the minimum number of sources necessary so that the
information spreads to all vertices of $G$ in $b_2(G)$ rounds. In addition to
general results, we find $b_2(G)$ and $t_2(G)$ for the classes of spiders and
wheels and show that their behavior differs with respect to these two
parameters. We also provide examples and prove upper bounds for these
parameters for Cartesian products of graphs. |
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DOI: | 10.48550/arxiv.2411.02050 |