The burning number of a graph G is the smallest number b such that the
vertices of G can be covered by balls of radii 0,1,β¦,bβ1. As
computing the burning number of a graph is known to be NP-hard, even on trees,
it is natural to consider polynomial time approximation algorithms for the
quantity. The best known approximation factor in the literature is 3 for
general graphs and 2 for trees. In this note we give a
2/(1βeβ2)+Ξ΅=2.313β¦-approximation algorithm for the burning
number of general graphs, and a PTAS for the burning number of trees and
forests. Moreover, we show that computing a
(35ββΞ΅)-approximation of the burning number of a general graph
G is NP-hard.Comment: 7 pages, no figures. Comments are welcome