The neighbour-sum-distinguishing edge-colouring game

Olivier Baudon (1) , Jakub Przybylo (2) , Mohammed Senhaji , Elzbieta Sidorowicz (3) , Eric Sopena (1) , Mariusz Wozniak (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 AGH UST - AGH University of Science and Technology [Krakow, PL]
3 Faculty of Mathematics, Computer Science and Econometric [Zielona Góra]

Let gamma : E(G) -> N* = N \ {0} be an edge colouring of a graph G and sigma(gamma) : V(G) -> N* the vertex colouring given by sigma(gamma)(v) = Sigma(e(sic)v)gamma(e) for every v is an element of V(G). A neighbour-sum-distinguishing edge-colouring of G is an edge colouring gamma such that for every edge uv in G, sigma(gamma)(u) not equal sigma(gamma)(v). The neighbour-sum-distinguishing edge-colouring game on G is the 2-player game defined as follows. The two players, Alice and Bob, alternately colour an uncoloured edge of G. Alice wins the game if, when all edges are coloured, the so-obtained edge colouring is a neighbour-sum-distinguishing edge-colouring of G. Otherwise, Bob wins. n this paper we study the neighbour-sum-distinguishing edge-colouring game on various classes of graphs. In particular, we prove that Bob wins the game on the complete graph K-n, n >= 3, whoever starts the game, except when n = 4. In that case, Bob wins the game on K-4 if and only if Alice starts the game

Mots clés: neighbour-sum-distinguishing edge-colouring game; edge-weighting; neighbour-sum-distinguishing edge-colouring

Domaines: Mathématique discrète [cs.DM]

Olivier Baudon, Jakub Przybylo, Mohammed Senhaji, Elzbieta Sidorowicz, Eric Sopena, et al.. The neighbour-sum-distinguishing edge-colouring game. Discrete Mathematics, 2017, 340 (7), pp.1564-1572. ⟨10.1016/j.disc.2017.02.019⟩. ⟨hal-01330532⟩