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- W4299368522 abstract "An incidence of a graph $G$ is a pair $(v,e)$ where $v$ is a vertex of $G$ and $e$ an edge incident to $v$. Two incidences $(v,e)$ and $(w,f)$ are adjacent whenever $v = w$, or $e = f$, or $vw = e$ or $f$. The incidence coloring game [S.D. Andres, The incidence game chromatic number, Discrete Appl. Math. 157 (2009), 1980-1987] 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 wins the game otherwise Bob wins the game. The incidence game chromatic number $i_g(G)$ of a graph $G$ is the minimum number of colors for which Alice has a winning strategy when playing the incidence coloring game on $G$. Andres proved that %$lceil 3/2 Delta(G)rceil le $i_g(G) le 2Delta(G) + 4k - 2$ for every $k$-degenerate graph $G$. %The arboricity $a(G)$ of a graph $G$ is the minimum number of forests into which its set of edges can be partitioned. %If $G$ is $k$-degenerate, then $a(G) le k le 2a(G) - 1$. We show in this paper that $i_g(G) le lfloorfrac{3Delta(G) - a(G)}{2}rfloor + 8a(G) - 2$ for every graph $G$, where $a(G)$ stands for the arboricity of $G$, thus improving the bound given by Andres since $a(G) le k$ for every $k$-degenerate graph $G$. Since there exists graphs with $i_g(G) ge lceilfrac{3Delta(G)}{2}rceil$, the multiplicative constant of our bound is best possible." @default.
- W4299368522 created "2022-10-02" @default.
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- W4299368522 date "2013-07-10" @default.
- W4299368522 modified "2023-10-10" @default.
- W4299368522 title "Incidence coloring game and arboricity of graphs" @default.
- W4299368522 hasPublicationYear "2013" @default.
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