Some graph classes satisfying acyclic edge colouring conjecture
نویسنده
چکیده
We present some classes of graphs which satisfy the acyclic edge colouring conjecture which states that any graph can be acyclically edge coloured with at most ∆ + 2 colours.
منابع مشابه
Three years of graphs and music : some results in graph theory and its applications
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...
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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...
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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...
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The acyclic edge colouring problem is extensively studied in graph theory. The corner-stone of this field is a conjecture of Alon et. al.[1] that a′(G) ≤ ∆(G) + 2. In that and subsequent work, a′(G) is typically bounded in terms of ∆(G). Motivated by this we introduce a term gap(G) defined as gap(G) = a′(G) − ∆(G). Alon’s conjecture can be rephrased as gap(G) ≤ 2 for all graphs G. In [5] it was...
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