voltarData: 26/08/2020
Título: Range-Relaxed Graceful Game.
Palestrante: Deise L. de Oliveira, IME/UFF.
Data: 26 de Agosto de 2020, 16 h.
Sala: Google Meet.
Resumo: The Range-Relaxed Graceful Game is played in a simple graph G, by two players, Alice and Bob, who alternately assign a previously unused label f(v) \in £={0, ..., k}, k >=|E(G)|, to a previously unlabeled vertex v \in V(G). Alice's goal is to end up with a vertex labeling of whole G where all of its edges have distinct labels and Bob's goal is to prevent it from happening. When k=|E(G)| the game is called graceful game. We investigate the graceful game in cartesian and corona products of graphs, and determine that Bob has a winning strategy in all investigated families independently of who starts the game. Additionally, we present the first results in the range-relaxed graceful game and prove that Alice wins on any simple graph G.
Obs. This joint work with Simone Dantas (IME-UFF) and Atílio G. Luiz (UFC), was accepted for presentation and publication in the CTW 2020 (18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization).