Lower bounds for (weak) sense of direction

A graph with n vertices and maximum degree cannot be given weak sense of direction using less than colours. It is known that n colours are always sufficient, but it has been conjectured that just +1 are really needed. On the contrary, we show that for sufficiently large n there are graphs requiring + (n/ log n) colours. We also give simple examples of small graphs requiring + 2 colours, which have been verified mechanically.

• Type: Conference
• Year: 2000
• Where: SIROCCO
• Authors: Paolo Boldi, Sebastiano Vigna
• Keywords: Colours, Maximum Degree, SIROCCO 2000, SIROCCO 2007, Weak Sense