Acyclic vertex coloring of graphs of maximum degree 5
نویسندگان
چکیده
منابع مشابه
Acyclic vertex coloring of graphs of maximum degree 5
An acyclic vertex coloring of a graph is a proper vertex coloring such that there are no bichromatic cycles. The acyclic chromatic number of G, denoted a(G), is the minimum number of colors required for acyclic vertex coloring of a graph G = (V,E). For a family F of graphs, the acyclic chromatic number of F , denoted by a(F ), is defined as the maximum a(G) over all the graphs G ∈ F . In this p...
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The acyclic chromatic number of a graph G, denoted a(G), is the minimum number of colors required to properly color the vertices of a graph such that there are no bichromatic cycles. The concept of acyclic coloring of a graph was introduced by [5] and is further studied in the last two decades in several works. Kostochka [6] proves that determining it is an NP-complete problem. Given the comput...
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An acyclic vertex coloring of a graph is a proper vertex coloring such that there are no bichromatic cycles. The acyclic chromatic number of G, denoted a(G), is the minimum number of colors required for acyclic vertex coloring of graph G = (V,E). For a family F of graphs, the acyclic chromatic number of F , denoted by a(F), is defined as the maximum a(G) over all the graphs G ∈ F . In this pape...
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A k-colouring of a graph G is a mapping c from the set of vertices of G to the set {1, . . . , k} of colours such that adjacent vertices receive distinct colours. Such a k-colouring is called acyclic, if for every two distinct colours i and j, the subgraph induced by all the edges linking a vertex coloured with i and a vertex coloured with j is acyclic. In other words, every cycle in G has at l...
متن کاملAcyclic coloring of graphs with maximum degree five
An acyclic k-coloring of a graph G is a proper vertex coloring of G which uses at most k colors such that the graph induced by the union of every two color classes is a forest. In this paper, we mainly prove that every 5-connected graph with maximum degree five is acyclically 8-colorable, improving partially [5].
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.10.024