| Title: | The burning game on graphs |
|---|
| Authors: | ID Chiarelli, Nina (Author)
ID Iršič Chenoweth, Vesna (Author)
ID Jakovac, Marko (Author)
ID Kinnersley, William B. (Author)
ID Mikalački, Mirjana (Author) |
|---|
| Files: |  PDF - Presentation file, download (989,58 KB)
MD5: DF60E7C58A690368A53C2CA36CEA2B36
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0012365X26000518
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| Abstract: | Motivated by the burning and cooling processes, the burning game is introduced. Two players (Burner and Staller) play the game on a graph $G$ by alternately selecting vertices of $G$ to burn; as in the burning process, burning vertices spread fire to unburned neighbors. Burner aims to burn all vertices of $G$ as quickly as possible, while Staller wants the process to last as long as possible. If both players play optimally, then the number of time steps needed to burn the whole graph $G$ is the game burning number $b_g(G)$ if Burner makes the first move, and the Staller-start game burning number $b'_g(G)$ if Staller starts. In this paper, basic bounds on $b_g(G)$ are given and several fundamental properties of the burning game established. Graphs with small game burning numbers are characterized and the game is studied on paths and cycles. An analogue of the burning number conjecture for the burning game is also considered. Finally, it is shown that the problem of determining whether or not $b_g(G) \le k$ is NP-hard. |
|---|
| Keywords: | burning game, burning number, Burner, Staller |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.05.2026 |
|---|
| Year of publishing: | 2026 |
|---|
| Number of pages: | 16 str. |
|---|
| Numbering: | Vol. 349, iss. 5, article no. 115027 |
|---|
| PID: | 20.500.12556/DiRROS-27609  |
|---|
| UDC: | 519.17:519.83 |
|---|
| ISSN on article: | 0012-365X |
|---|
| DOI: | 10.1016/j.disc.2026.115027 |
|---|
| COBISS.SI-ID: | 268412163 |
|---|
| Note: |
|
|---|
| Publication date in DiRROS: | 16.02.2026 |
|---|
| Views: | 209 |
|---|
| Downloads: | 69 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
