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|a E 1.99:1841468
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|a E 1.99:1841468
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|a Improved Bounds for Burning Fence Graphs
|h [electronic resource]
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|a Oak Ridge, Tenn. :
|b Oak Ridge National Laboratory ;
|a Oak Ridge, Tenn. :
|b Distributed by the Office of Scientific and Technical Information, U.S. Department of Energy,
|c 2021.
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|a Size: p. 2761-2773 :
|b digital, PDF file.
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|a text
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|a online resource
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|a Published through Scitech Connect.
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|a 08/06/2021.
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|a "Journal ID: ISSN 0911-0119."
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|a Bonato, Anthony ; English, Sean ; Kay, Bill ; Moghbel, Daniel ;
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|a USDOE.
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|a 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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|b AC05-00OR22725.
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|a Graphs
|2 local.
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|a Burning number
|2 local.
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|a Cartesian grids
|2 local.
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|a Fence graphs
|2 local.
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|a Bounds
|2 local.
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|a Oak Ridge National Laboratory.
|4 res.
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|a United States.
|b Department of Energy.
|b Office of Scientific and Technical Information
|4 dst.
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|u https://www.osti.gov/servlets/purl/1841468
|z Full Text (via OSTI)
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|a .b128258536
|b 02-28-23
|c 12-08-22
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|p Can circulate
|a University of Colorado Boulder
|b Online
|c Online
|d Online
|e E 1.99:1841468
|h Superintendent of Documents classification
|i web
|n 1
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