7 papers
Thresholds for the biased Maker-Breaker domination games
Boštjan Brešar, Csilla Bujtás, Pakanun Dokyeesun +1
In the -biased Maker-Breaker domination game, two players alternately select unplayed vertices in a graph such that Dominator selects and Staller selects vertice…
Distance mutual-visibility coloring: relations with (total) domination, exact distance graphs and graph products
Saneesh Babu, Boštjan Brešar, Aparna Lakshmanan S +1
The concept of mutual-visibility (MV) has been extended in several directions. A vertex subset of a graph is a -distance mutual-visibility (DMV) set if for any two ve…
Monophonic number of Kneser graphs and strongly 2-monophonic graphs
BoÅ¡tjan BreÅ¡ar, MarÃa Gracia Cornet, Tanja Dravec
Given a graph a set is called monophonic if every vertex in lies on some induced path between two vertices in . The monophonic number, , of , wh…
Isolation number: Cartesian and lexicographic products and generalized SierpiÅski graphs
Bostjan Bresar, Tanja Dravec, Daniel P. Johnston +3
The isolation number of a graph is the minimum cardinality of a set such that the subgraph induced by the vertices that are not in the union of the clos…
Total -coalition: bounds, exact values and an application to double coalition
Boštjan Brešar, Sandi Klavžar, Babak Samadi
Let $G=\big{(}V(G),E(G)\big{)}$ be a graph with minimum degree . A subset is called a total -dominating set if every vertex in has at least neighbor…
Independent mutual-visibility coloring and related concepts
Boštjan Brešar, Iztok Peterin, Babak Samadi +1
Given a graph , a subset is a mutual-visibility (MV) set if for every , there exists a -geodesic whose internal vertices are not in . We inve…