Acyclic edge colorings of graphs
نویسندگان
چکیده
منابع مشابه
Acyclic edge colorings of graphs
A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a′(G), is the least number of colors in an acyclic edge coloring of G. For certain graphs G, a′(G) ≥ ∆(G) + 2 where ∆(G) is the maximum degree in G. It is known that a′(G) ≤ 16∆(G) for any graph G (see [2],[10]). We prove that there exists a const...
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A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G is the least number of colors in an acyclic edge coloring of G. In this paper, it is proved that the acyclic edge chromatic number of a planar graph G is at most ∆(G)+2 if G contains no i-cycles, 4≤ i≤ 8, or any two 3-cycles are not incident with a common vertex and ...
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In this paper, we introduce the new notion of acyclic improper colorings of graphs. An improper coloring of a graph G is a mapping c from the set of vertices of G to a set of colors such that for every color i, the subgraph induced by the vertices with color i satisses some property depending on i. Such an improper coloring is acyclic if for every two distinct colors i and j, the subgraph induc...
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It is shown that a planar graph can be partitioned into three linear forests. The sharpness of the result is also considered. In 1969, Chartrand and Kronk [2] showed that the vertex arboricity of a planar graph is at most 3. In other words, the vertex set of a planar graph can be partitioned into three sets each inducing a forest. In this paper we present an improvement on this result: that the...
متن کاملmodular edge colorings of mycielskian graphs
let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$ ($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same. the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2001
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.1010