Three years of graphs and music : some results in graph theory and its applications
نویسنده
چکیده
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 graphs with girth at least 5. We also show that χa(G) ≤ ∆(G)+ 12 for all planar G, which improves a previous result by Fiedorowicz et al. [15].
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