Decomposing a graph into forests

The fractional arboricity @c"f(G) of a graph G is the maximum of the ratio |E(G[X])|/(|X|-1) over all the induced subgraphs G[X] of G. In this paper, we propose a conjecture which says that every graph G with @c"f(G)=0, there is a graph G with @c"f(G)

[1]  D. Gonçalves,et al.  Covering planar graphs with forests, one having a bounded maximum degree , 2008, Electron. Notes Discret. Math..

[2]  Xuding Zhu The Game Coloring Number of Planar Graphs , 1999, J. Comb. Theory, Ser. B.

[3]  Xuding Zhu,et al.  Edge-partitions of planar graphs and their game coloring numbers , 2002 .

[4]  Alexandr V. Kostochka,et al.  Decomposition of Sparse Graphs into Forests and a Graph with Bounded Degree , 2013, J. Graph Theory.

[5]  Yingqian Wang,et al.  Decomposing a planar graph with girth at least 8 into a forest and a matching , 2011, Discret. Math..

[6]  André Raspaud,et al.  Decomposition of sparse graphs, with application to game coloring number , 2010, Discret. Math..

[7]  C. Nash-Williams Decomposition of Finite Graphs Into Forests , 1964 .

[8]  C. Payan,et al.  Equilibrium graphs and rational trees , 1986 .

[9]  Alexandr V. Kostochka,et al.  Decomposing a planar graph with girth 9 into a forest and a matching , 2008, Eur. J. Comb..

[10]  Oleg V. Borodin,et al.  Decomposing a planar graph into a forest and a subgraph of restricted maximum degree. , 2007 .

[11]  Hong-Jian Lai,et al.  Fractional Arboricity, Strength, and Principal Partitions in Graphs and Matroids , 1992, Discret. Appl. Math..

[12]  Hans L. Bodlaender On the Complexity of Some Coloring Games , 1991, Int. J. Found. Comput. Sci..

[13]  S. Hakimi On the degrees of the vertices of a directed graph , 1965 .

[14]  Xingxing Yu,et al.  Covering planar graphs with forests , 2005, J. Comb. Theory, Ser. B.

[15]  Xuding Zhu,et al.  Refined activation strategy for the marking game , 2008, J. Comb. Theory B.

[16]  Daniel Gonçalves,et al.  Etudes de différents problèmes de partition de graphes , 2006 .

[17]  U. Faigle,et al.  On the game chromatic number of some classes of graphs , 1991 .