منابع مشابه
The game of arboricity
Using a fixed set of colors C, Ann and Ben color the edges of a graph G so that no monochromatic cycle may appear. Ann wins if all edges of G have been colored, while Ben wins if completing a coloring is not possible. The minimum size of C for which Ann has a winning strategy is called the game arboricity of G, denoted by Ag(G). We prove that Ag(G) ≤ 3k for any graph G of arboricity k, and that...
متن کاملIncidence Coloring Game and Arboricity of Graphs
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, alte...
متن کاملLinear Arboricity and Linear k-Arboricity of Regular Graphs
We find upper bounds on the linear k-arboricity of d-regular graphs using a probabilistic argument. For small k these bounds are new. For large k they blend into the known upper bounds on the linear arboricity of regular graphs.
متن کاملThe Linear Arboricity of Graphs
A linear forest is a forest in which each connected component is a path. The linear arboricity la(G) of a graph G is the minimum number of linear forests whose union is the set of all edges of G. The linear arboricity conjecture asserts that for every simple graph G with maximum degree A = A(G), Although this conjecture received a considerable amount of attention, it has been proved only for A ...
متن کاملStar arboricity
A star forest is a forest all of whose components are stars. The star arboricity, st(G) of a graph G is the minimum number of star forests whose union covers all the edges of G. The arboricity, A(G), of a graph G is the minimum number of forests whose union covers all the edges of G. Clearly st(G) > A(G). In fact, Algor and Alon have given examples which show that in some cases st(G) can be as ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.07.066