منابع مشابه
Acyclic colouring of graphs
A vertex colouring of a graph G is called acyclic if no two adjacent vertices have the same colour and there is no two-coloured cycle in G. The acyclic chromatic number of G, denoted by A(G), is the least number of colours in an acyclic colouring of G. We show that if G has maximum degree d then A(G) = O(d 4 3 ) as d → ∞. This settles a problem of Erdős who conjectured, in 1976, that A(G) = o(d...
متن کاملSome graph classes satisfying acyclic edge colouring conjecture
We present some classes of graphs which satisfy the acyclic edge colouring conjecture which states that any graph can be acyclically edge coloured with at most ∆ + 2 colours.
متن کاملAcyclic, Star and Oriented Colourings of Graph Subdivisions
Let G be a graph with chromatic number χ(G). A vertex colouring of G is acyclic if each bichromatic subgraph is a forest. A star colouring of G is an acyclic colouring in which each bichromatic subgraph is a star forest. Let χa(G) and χs(G) denote the acyclic and star chromatic numbers of G. This paper investigates acyclic and star colourings of subdivisions. Let G′ be the graph obtained from G...
متن کاملAcyclic colouring of 1-planar graphs
A graph is 1-planar if it can be drawn on the plane in such a way that every edge crosses at most one other edge. We prove that the acyclic chromatic number of every 1-planar graph is at most 20.
متن کاملAcyclic Edge Colouring of Partial 2-Trees
An acyclic edge colouring of a graph is a proper edge colouring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge colouring using k colours and it is denoted by a′(G). Here, we obtain tight estimates on a′(G) for nontrivial subclasses of the family of 2-degenerate graphs. Specifically, we obtain values of...
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ژورنال
عنوان ژورنال: International Journal of Computer Applications
سال: 2010
ISSN: 0975-8887
DOI: 10.5120/1135-1486