Improved Bounds for Burning Fence Graphs [electronic resource]
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| Online Access: |
Full Text (via OSTI) |
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| Format: | Government Document Electronic eBook |
| Language: | English |
| Published: |
Oak Ridge, Tenn. : Oak Ridge, Tenn. :
Oak Ridge National Laboratory ; Distributed by the Office of Scientific and Technical Information, U.S. Department of Energy,
2021.
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| Abstract: | Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire breaks out at a vertex, and the fire spreads to all vertices that are adjacent to a burning vertex. Additionally, the burning number of a graph <i>G</i> is the minimum number of rounds necessary for each vertex of <i>G</i> to burn. We consider the burning number of the <span class="mathjax-tex">\(m \times n\)</span> Cartesian grid graphs, written <span class="mathjax-tex">\(G_{m,n}\)</span>. For <span class="mathjax-tex">\(m = \omega (\sqrt{n})\)</span>, the asymptotic value of the burning number of <span class="mathjax-tex">\(G_{m,n}\)</span> was determined, but only the growth rate of the burning number was investigated in the case <span class="mathjax-tex">\(m = O(\sqrt{n})\)</span>, which we refer to as fence graphs. We provide new explicit bounds on the burning number of fence graphs <span class="mathjax-tex">\(G_{c\sqrt{n},n}\)</span>, where <span class="mathjax-tex">\(c > 0\)</span> |
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| Item Description: | Published through Scitech Connect. 08/06/2021. "Journal ID: ISSN 0911-0119." Bonato, Anthony ; English, Sean ; Kay, Bill ; Moghbel, Daniel ; USDOE. |
| Physical Description: | Size: p. 2761-2773 : digital, PDF file. |