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. The burning number of a graph G is the minimum number of rounds necessary for each vertex of G to burn. We consider the burning number of the \(m \times n\) Cartesian grid graphs, written \(G_{m,n}\). For \(m = \omega (\sqrt{n})\), the asymptotic value of the burning number of \(G_{m,n}\) was determined, but only the growth rate of the burning number was investigated in the case \(m = O(\sqrt{n})\), which we refer to as fence graphs. We provide new explicit bounds on the burning number of fence graphs \(G_{c\sqrt{n},n}\), where \(c > 0\).

图燃烧研究了一种传染病（建模为一组火灾）在图中传播的速度。燃烧过程以同步的、离散的轮次进行。在每一轮中，一个顶点会发生火灾，并且火焰会蔓延到与燃烧的顶点相邻的所有顶点。的曲线图的燃烧数目ģ是必要的每个顶点轮的最小数目ģ燃烧。我们考虑\(m \times n\)笛卡尔网格图的燃烧数，写作\(G_{m,n}\)。对于\(m = \omega (\sqrt{n})\)，确定了\(G_{m,n}\)的燃烧数的渐近值，但仅研究了燃烧数的增长率案子\(m = O(\sqrt{n})\)，我们称之为栅栏图。我们为栅栏图\(G_{c\sqrt{n},n}\)的燃烧数量提供了新的明确界限，其中\(c > 0\)。