Burning and w-burning of geometric graphs
Graph burning runs on discrete time-steps. The aim is to burn all the vertices in a given graph using a minimum number of time-steps. This number is known to be the burning number of the graph. The spread of social influence, an alarm, or a social contagion can be modeled using graph burning. The le...
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| Published in: | Discrete Applied Mathematics Vol. 336; pp. 83 - 98 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
15-09-2023
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | Graph burning runs on discrete time-steps. The aim is to burn all the vertices in a given graph using a minimum number of time-steps. This number is known to be the burning number of the graph. The spread of social influence, an alarm, or a social contagion can be modeled using graph burning. The less the burning number, the faster the spread.
It is well-known that the optimal burning of general graphs is NP-complete. Further, graph burning has been shown to be NP-complete on a vast majority classes of graphs. Approximation results also exist for several graph classes. In this article, we show that the burning problem is NP-complete on connected interval graphs and permutation graphs. We also study the burning properties of grids. More precisely, we show that the lower bound of the burning number of a grid (l×b) is at least (l×b)13. We provide a 2-approximation for burning a square grid.
We extend the study of the w-burning problem, a variation of the graph burning problem where we allow a constant w number of vertices to be burnt in any time-step. We prove that w-burning of interval, spider, and permutation graphs are NP-complete for any constant w. We also provide a 2-approximation for the w-burning problem on trees. |
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| ISSN: | 0166-218X 1872-6771 |
| DOI: | 10.1016/j.dam.2023.03.026 |