On star and caterpillar arboricity
نویسندگان
چکیده
منابع مشابه
On star and caterpillar arboricity
We give new bounds on the star arboricity and the caterpillar arboricity of planar graphs with given girth. One of them answers an open problem of Gyárfás and West: there exist planar graphs with track number 4. We also provide new NP-complete problems.
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 ...
متن کاملWDM and Directed Star Arboricity
A digraph is m-labelled if every arcs is labelled by an integer in {1, . . . , m}. Motivated by wavelength assignment for multicasts in optical star networks, we study n-fiber colourings of labelled digraph which are colourings of the arcs of D such that at each vertex v, for each colour in λ, in(v, λ) + out(v, λ) ≤ n with in(v, λ) the number of arcs coloured λ entering v and out(v, λ) the numb...
متن کاملOn the star arboricity of hypercubes
A hypercube Qn is a graph in which the vertices are all binary vectors of length n, and two vertices are adjacent if and only if their components differ in exactly one place. A galaxy or a star forest is a union of vertex disjoint stars. The star arboricity of a graph G, sa(G), is the minimum number of galaxies which partition the edge set of G. In this paper among other results, we determine t...
متن کاملOn incidence coloring and star arboricity of graphs
In this note we show that the concept of incidence coloring introduced in [BM] is a special case of directed star arboricity, introduced in [AA]. A conjecture in [BM] concerning asmyptotics of the incidence coloring number is solved in the negative following an example in [AA]. We generalize Theorem 2.1 of [AMR] concerning the star arboricity of graphs to the directed case by a slight modificat...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.01.041