7 citations · 10 across the 11 of their papers we have counts for
7 papers · 1 filter
On the Burning Game: Nordhaus-Gaddum Bounds and Graph Products
Nina Chiarelli, Vesna Iršič Chenoweth, Marko Jakovac +2
We continue research on the burning game on graphs. Given a graph , two players, Burner and Staller, take turns in selecting vertices of to burn. All burned vertices spread…
Patrolling cop vs omniscient robber
Nina Chiarelli, Paul Dorbec, Miloš Stojaković +1
We study a variant of the classical Cops and Robbers game with one cop and one robber. The cop follows a fixed walk on the graph, called a patrol, that is chosen before the game be…
On -Roman graphs: complexity of recognition and the case of split graphs
Kenny Bešter Štorgel, Nina Chiarelli, Lara Fernández +4
For a positive integer , a -Roman dominating function of a graph is a function satisfying $\sum_{u\in N(v)} f(u) \geq…
Strong cliques in diamond-free graphs
Nina Chiarelli, Berenice Martínez Barona, Martin Milanič +2
A strong clique in a graph is a clique intersecting all inclusion-maximal stable sets. Strong cliques play an important role in the study of perfect graphs. We study strong cliques…
Linear separation of connected dominating sets in graphs
Nina Chiarelli, Martin Milanič
A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph. Following analogous studies in the literature related to independent sets,…
Equistarable bipartite graphs
Endre Boros, Nina Chiarelli, Martin Milanič
Recently, Milanič and Trotignon introduced the class of equistarable graphs as graphs without isolated vertices admitting positive weights on the edges such that a subset of edges…
Total Domishold Graphs: a Generalization of Threshold Graphs, with Connections to Threshold Hypergraphs
Nina Chiarelli, Martin Milanic
A total dominating set in a graph is a set of vertices such that every vertex of the graph has a neighbor in the set. We introduce and study graphs that admit non-negative real wei…