Strong edge-colouring of sparse planar graphs
نویسندگان
چکیده
A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degree∆ has a strong edge-colouring with at most 4∆ + 4 colours. We show that 3∆ + 1 colours suffice if the graph has girth 6, and 4∆ colours suffice if ∆ ≥ 7 or the girth is at least 5. In the last part of the paper, we raise some questions related to a long-standing conjecture of Vizing on proper edge-colouring of planar graphs.
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 179 شماره
صفحات -
تاریخ انتشار 2014