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An incidence of a graph G is a pair (v, e) where v is a vertex of G and e an edge incident to v.] is a variation of the ordinary coloring game where the two players, Alice and Bob, alternately color the incidences of a graph, using a given number of colors, in such a way that adjacent incidences get distinct colors. If the whole graph is colored then Alice… (More)

We denote by χ g (G) the game chromatic number of a graph G, which is the smallest number of colors Alice needs to win the coloring game on G. We know from Montassier et al. a planar graph with girth at least 8 into a forest and a matching, Discrete Maths, 311:844-849, 2011] that planar graphs with girth at least 8 have game chromatic number at most 5. One… (More)

The incidence coloring game has been introduced in [S. 1987] as a variation of the ordinary coloring game. The incidence game chromatic number ι g (G) of a graph G is the minimum number of colors for which Alice has a winning strategy when playing the incidence coloring game on G. we proved that ι g (G) ≤ ⌊ 3∆(G)−a 2 ⌋ + 8a − 1 for every graph G with… (More)

- C. Charpentier
- 2014

The square G 2 of a graph G is the graph obtained from G by adding an edge between every pair of vertices having a common neighbor. A proper coloring of G 2 is also called a 2-distance coloring of G. The maximum average degree Mad(G) of a graph G is the maximum among the average degrees of the subgraphs of G, i.e. Mad(G) = max 2|E(H)| V (H) |H ⊆ G. Graphs… (More)

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