d-Regular graphs of acyclic chromatic index at leastd+2
نویسندگان
چکیده
منابع مشابه
d-Regular Graphs of Acyclic Chromatic Index
An acyclic edge coloring of a graph is a proper edge coloring 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 coloring using k colors and is denoted by a′(G). It was conjectured by Alon, Sudakov and Zaks (and earlier by Fiamcik) that a′(G)≤ +2, where = (G) denotes the maximum degree of the graph. Alon e...
متن کاملd-Regular graphs of acyclic chromatic index at least d+2
An acyclic edge coloring of a graph is a proper edge coloring 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 coloring using k colors and is denoted by a(G). It was conjectured by Alon, Sudakov and Zaks (and earlier by Fiamcik) that a(G) ≤ ∆ + 2, where ∆ = ∆(G) denotes the maximum degree of the graph. A...
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An acyclic edge coloring of a graph is a proper edge coloring 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 coloring using k colors and is denoted by a′(G). A graph G is called fully subdivided if it is obtained from another graph H by replacing every edge by a path of length at least two. Fully subdi...
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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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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: Journal of Graph Theory
سال: 2010
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.20422