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Maker-Breaker total domination number | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 16، دوره 11، شماره 4، اسفند 2026، صفحه 1249-1263 اصل مقاله (431.29 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30824.2634 | ||
| نویسندگان | ||
| Athira Divakaran1؛ Tijo James2؛ Sandi Klavžar* 3، 4، 5؛ Latha S Nair1 | ||
| 1Department of Mathematics, Mar Athanasius College, Kothamangalam, India | ||
| 2Department of Mathematics, Pavanatma College, Murickassery, India | ||
| 3Faculty of Mathematics and Physics, University of Ljubljana, Slovenia | ||
| 4Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia | ||
| 5Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia | ||
| چکیده | ||
| The Maker-Breaker total domination number, $\gamma_{\rm MBT}(G)$, of a graph $G$ is introduced as the minimum number of moves of Dominator to win the Maker-Breaker total domination game, provided that he has a winning strategy and is the first to play. The Staller-start Maker-Breaker total domination number, $\gamma_{\rm MBT}'(G)$, is defined analogously for the game in which Staller starts. Upper and lower bounds on $\gamma_{\rm MBT}(G)$ and on $\gamma_{\rm MBT}'(G)$ are provided and demonstrated to be sharp. It is proved that for any pair of integers $(k,\ell)$ with $2\leq k\leq \ell$, (i) there exists a connected graph $G$ with $\gamma_{\rm MB}(G)=k$ and $\gamma_{\rm MBT}(G)=\ell$, (ii) there exists a connected graph $G'$ with $\gamma_{\rm MB}'(G')=k$ and $\gamma_{\rm MBT}'(G')=\ell$, and (iii) there there exists a connected graph $G''$ with $\gamma_{\rm MBT}(G'')=k$ and $\gamma_{\rm MBT}'(G'')=\ell$. Here, $\gamma_{\rm MB}$ and $\gamma_{\rm MB}'$ are corresponding invariants for the Maker-Breaker domination game. | ||
| کلیدواژهها | ||
| Positional game؛ Maker–Breaker domination game؛ Maker–Breaker total domination game؛ Maker–Breaker total domination number | ||
| مراجع | ||
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