20.500.12556/RUL-155607 Maker-Breaker domination game on trees when Staller wins In the Maker-Breaker domination game played on a graph $G$, Dominator's goal is to select a dominating set and Staller's goal is to claim a closed neighborhood of some vertex. We study the cases when Staller can win the game. If Dominator (resp., Staller) starts the game, then $\gamma_{\rm SMB}(G)$ (resp., $\gamma_{\rm SMB}'(G)$) denotes the minimum number of moves Staller needs to win. For every positive integer $k$, trees $T$ with $\gamma_{\rm SMB}'(T)=k$ are characterized and a general upper bound on $\gamma_{\rm SMB}'$ is proved. Let $S = S(n_1,\dots, n_\ell)$ be the subdivided star obtained from the star with $\ell$ edges by subdividing its edges $n_1-1, \ldots, n_\ell-1$ times, respectively. Then $\gamma_{\rm SMB}'(S)$ is determined in all the cases except when $\ell\ge 4$ and each $n_i$ is even. The simplest formula is obtained when there are at least two odd $n_i$s. If ▫$n_1$▫ and $n_2$ are the two smallest such numbers, then $\gamma_{\rm SMB}'(S(n_1,\dots, n_\ell))=\lceil \log_2(n_1+n_2+1)\rceil$▫. For caterpillars, exact formulas for $\gamma_{\rm SMB}$ and for $\gamma_{\rm SMB}'$ are established. domination game Maker-Breaker game Maker-Breaker domination game hypergraphs trees subdivided stars caterpillars dominacijska igra igra izdelovalec-lomilec dominacijska igra izdelovalec-lomilec hipergrafi drevesa subdividirane zvezde gosenice true false true Angleški jezik Slovenski jezik Članek v reviji 2024-04-08 11:29:34 2024-04-08 11:29:37 2024-04-09 03:46:01 0000-00-00 00:00:00 2023 0 0 21 str. no. 2, [article no.] 12 Vol. 25 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-01-01 519.17 1365-8050 10.46298/dmtcs.10515 164065283 2212.06530.pdf 2212.06530.pdf 1 4F25DFACA34AE0F4CAF70CC07280641C ed0b5ea4d65bba8f9ce74afe857c7e7bdd533dc137278a86b90f52af1e268e08 ccdaca44-f58a-11ee-937a-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=182583 https://dmtcs.episciences.org/12202 1 85569af5-f58a-11ee-937a-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=182582 Fakulteta za matematiko in fiziko 0 0 0