More Lower Bounds for Weak Sense of Direction: The Case of Regular Graphs
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چکیده
A graph G with n vertices and maximum degree 1G cannot be given weak sense of direction using less than 1G colours. It is known that n colours are always sufficient, and it was conjectured that just 1G + 1 are really needed, that is, one more colour is sufficient. Nonetheless, it has just been shown [2] that for sufficiently large n there are graphs requiring ω(n/ log n) more colours than 1G . In this paper, using recent results in asymptotic graph enumeration, we show not only that (somehow surprisingly) the same bound holds for regular graphs, but also that it can be improved to (n log log n/ log n). We also show that (
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تاریخ انتشار 2000