The vertex linear arboricity of distance graphs

A distance graph is a graph G(R,D) with the set of all points of the real line as vertex set and two vertices u,[email protected]?R are adjacent if and only if |u-v|@?D where the distance set D is a subset of the positive real numbers. Here, the vertex linear arboricity of G(R,D) is determined when D is an interval between 1 and @d. In particular, the vertex linear arboricity of integer distance graphs G(D) is discussed, too.

[1]  Arnfried Kemnitz,et al.  Coloring of integer distance graphs , 1998, Discret. Math..

[2]  Paul Erdös,et al.  Colouring the real line , 1985, J. Comb. Theory B.

[3]  K. S. Poh.  On the linear vertex-arboricity of a planar graph , 1990, J. Graph Theory.

[4]  Paul Erdös,et al.  Colouring prime distance graphs , 1990, Graphs Comb..

[5]  Wayne Goddard,et al.  Acyclic colorings of planar graphs , 1991, Discret. Math..

[6]  Xuding Zhu,et al.  Distance Graphs and T-Coloring , 1999, J. Comb. Theory B.

[7]  Jin Akiyama,et al.  Path chromatic numbers of graphs , 1989, J. Graph Theory.

[8]  Arnfried Kemnitz,et al.  Chromatic numbers of integer distance graphs , 2001, Discret. Math..

[9]  Margit Voigt,et al.  Chromatic Number of Prime Distance Graphs , 1994, Discret. Appl. Math..

[10]  Makoto Matsumoto,et al.  Bounds for the vertex linear arboricity , 1990, J. Graph Theory.

[11]  Jian-Liang Wu,et al.  The Vertex Linear Arboricity of an Integer Distance Graph with a Special Distance Set , 2006, Ars Comb..