Acyclic edge colouring of planar graphs without short cycles
نویسندگان
چکیده
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 G contains no i-cycles, i = 4 and 5.
منابع مشابه
About acyclic edge colourings of planar graphs
Let G = (V,E) be any finite simple graph. A mapping C : E → [k] is called an acyclic edge k-colouring of G, if any two adjacent edges have different colours and there are no bichromatic cycles in G. In other words, for every pair of distinct colours i and j, the subgraph induced by all the edges which have either colour i or j is acyclic. The smallest number k of colours, such that G has an acy...
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A proper edge-colouring with the property that every cycle contains edges of at least three distinct colours is called an acyclic edge-colouring. The acyclic chromatic index of a graph G, denoted χa(G), is the minimum k such that G admits an acyclic edge-colouring with k colours. We conjecture that if G is planar and ∆(G) is large enough then χa(G) = ∆(G). We settle this conjecture for planar g...
متن کاملAcyclic edge colouring of plane graphs
A proper edge-colouring with the property that every cycle contains edges of at least three distinct colours is called an acyclic edge-colouring. The acyclic chromatic index of a graph G, denoted χa(G), is the minimum k such that G admits an acyclic edge-colouring with k colours. We conjecture that if G is planar and ∆(G) is large enough then χa(G) = ∆(G). We settle this conjecture for planar g...
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A proper edge-colouring with the property that every cycle contains edges of at least three distinct colours is called an acyclic edge-colouring. The acyclic chromatic index of a graph G, denoted χa(G) is the minimum k such that G admits an acyclic edge-colouring with k colours. We conjecture that if G is planar and ∆(G) is large enough then χa(G) = ∆(G). We settle this conjecture for planar gr...
متن کاملAcyclic Edge Colorings of Planar Graphs Without Short Cycles∗
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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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010