5 papers · 1 filter
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…
Cayley trees and increasing 1,2-trees: let's twist!
Julien Courtiel, Matthieu Dien, Paul Dorbec
An increasing 1,2-tree is a labeled graph formed by starting with a vertex and then repeatedly attaching a leaf to a vertex or a triangle to an edge, the labeling of the vertices c…
An exploration of the balance game
Paul Dorbec, Michael A. Henning, Zsolt Tuza +1
The balance game is played on a graph by two players, Admirable (A) and Impish (I), who take turns selecting unlabeled vertices of . Admirable labels the selected vertices b…
Cutting Lemma and Union Lemma for the Domination Game
Paul Dorbec, Michael A. Henning, Sandi Klavžar +1
Two new techniques are introduced into the theory of the domination game. The cutting lemma bounds the game domination number of a partially dominated graph with the game dominatio…
Ice sliding games
Paul Dorbec, Eric Duchêne, André Fabbri +3
This paper deals with sliding games, which are a variant of the better known pushpush game. On a given structure (grid, torus...), a robot can move in a specific set of directions,…