20.500.12556/DiRROS-29002 Criticality for Maker-Breaker domination games with predomination A predominated graph is a pair $(G,D)$, where $G$ is a graph and the vertices in $D\subseteq V(G)$ are considered already dominated. Maker-Breaker domination game critical (MBD critical) predominated graphs are introduced as the predominated graphs $(G,D)$ on which Staller wins the game, but Dominator wins on $(G, D \cup \{v\})$ for every vertex $v \in V(G) \setminus D$. Tools are developed for handling the Maker-Breaker domination game on trees which lead to a characterization of Staller-win predominated trees. MBD critical predominated trees are characterized and an algorithm is designed which verifies in linear time whether a given predominated tree is MBD critical. A large class of MBD critical predominated cacti is presented and Maker-Breaker critical hypergraphs are constructed. domination games Maker-Breaker games Maker-Breaker domination game predomination hypergraph dominacijske igre igre izdelovalec-lomilec dominacijska igra izdelovalec-lomilec predominacija hipergrafi true false true Angleški jezik Slovenski jezik Neznano 2026-04-16 11:11:04 2026-04-16 11:11:05 2026-04-17 03:55:05 0000-00-00 00:00:00 2026 0 0 str. 483-506 no. 2 Vol. 46 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 519.17 1234-3099 10.7151/dmgt.2615 275411971 DMGT-2615.pdf DMGT-2615.pdf 1 66742E2FD146175ACDEAA65A9A3F3F73 1ad7e582e314a6d24be96d6970793f0b37e8a9974294dc1b76705ed96e5e9eb3 4258d437-3975-11f1-9cc3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43292 https://www.dmgt.uz.zgora.pl/publish/article.php?doi=2615 1 377d4eff-3974-11f1-9cc3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=43291 Inštitut za matematiko, fiziko in mehaniko 0 0 0