For connected G, G^k has a (k+1)^+-branching spanning tree whose burning number is at most ceil(sqrt(4(k-1)n/k^2)), yielding the same bound for b(G^k) and the asymptotic b(G^k) <= (1+o(1))sqrt(n/k).
5 Anthony Bonato, Jeannette Janssen, and Elham Roshanbin
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Burning Graph Powers and Branching Trees
For connected G, G^k has a (k+1)^+-branching spanning tree whose burning number is at most ceil(sqrt(4(k-1)n/k^2)), yielding the same bound for b(G^k) and the asymptotic b(G^k) <= (1+o(1))sqrt(n/k).