Further Results on Acyclic Chromatic Number
نویسندگان
چکیده
منابع مشابه
Further result on acyclic chromatic index of planar graphs
An acyclic edge coloring of a graph G is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index χa(G) of a graph G is the least number of colors in an acyclic edge coloring of G. It was conjectured that χa(G) ≤ ∆(G) + 2 for any simple graph G with maximum degree ∆(G). In this paper, we prove that every planar graph G admits an acyclic edg...
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Suppose that T is an acyclic r-uniform hypergraph, with r ≥ 2. We define the (t-color) chromatic Ramsey number χ(T, t) as the smallest m with the following property: if the edges of any m-chromatic r-uniform hypergraph are colored with t colors in any manner, there is a monochromatic copy of T . We observe that χ(T, t) is well defined and ⌈ R(T, t)− 1 r − 1 ⌉ + 1 ≤ χ(T, t) ≤ |E(T )| + 1 where R...
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An acyclic coloring of a graph G is a proper coloring of the vertex set of G such that G contains no bichromatic cycles. The acyclic chromatic number of a graph G is the minimum number k such that G has an acyclic coloring with k colors. In this paper, acyclic colorings of Hamming graphs, products of complete graphs, are considered.
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It is known (Bollobás [4]; Kostochka and Mazurova [13]) that there exist graphs of maximum degree ∆ and of arbitrarily large girth whose chromatic number is at least c∆/ log ∆. We show an analogous result for digraphs where the chromatic number of a digraph D is defined as the minimum integer k so that V (D) can be partitioned into k acyclic sets, and the girth is the length of the shortest cyc...
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The r-acyclic edge chromatic number of a graph is defined to be the minimum number of colours required to produce an edge colouring of the graph such that adjacent edges receive different colours and every cycle C has at least min(|C|, r) colours. We show that (r − 2)d is asymptotically almost surely (a.a.s.) an upper bound on the r-acyclic edge chromatic number of a random d-regular graph, for...
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ژورنال
عنوان ژورنال: Open Journal of Discrete Mathematics
سال: 2013
ISSN: 2161-7635,2161-7643
DOI: 10.4236/ojdm.2013.32019