Acyclic 6-coloring of graphs with maximum degree 5 and small maximum average degree
نویسندگان
چکیده
منابع مشابه
Acyclic 6-coloring of graphs with maximum degree 5 and small maximum average degree
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...
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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 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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A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...
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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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An incidence of an undirected graph G is a pair (v, e) where v is a vertex of G and e an edge of G incident with v. Two incidences (v, e) and (w, f) are adjacent if one of the following holds: (i) v = w, (ii) e = f or (iii) vw = e or f . An incidence coloring of G assigns a color to each incidence of G in such a way that adjacent incidences get distinct colors. In 2005, Hosseini Dolama et al. [...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2013
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1665