On parcimonious edge-colouring of graphs with maximum degree three
نویسندگان
چکیده
In a graph G of maximum degree ∆ let γ denote the largest fraction of edges that can be ∆ edge-coloured. Albertson and Haas showed that γ ≥ 13 15 when G is cubic . We show here that this result can be extended to graphs with maximum degree 3 with the exception of a graph on 5 vertices. Moreover, there are exactly two graphs with maximum degree 3 (one being obviously the Petersen graph) for which γ = 13 15 . This extends a result given by Steffen. These results are obtained by using structural properties of the so called δ-minimum edge colourings for graphs with maximum degree 3.
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 29 شماره
صفحات -
تاریخ انتشار 2013