Antibandwidth of complete -ary trees

The antibandwidth problem is to label vertices of a n -vertex graph injectively by 1 , 2 , 3 , … n , so that the minimum difference between labels of adjacent vertices is maximised. The problem is motivated by the obnoxious facility location problem, radiocolouring, work and game scheduling and is dual to the well known bandwidth problem. We prove exact results for the antibandwidth of complete k -ary trees, k even, and estimate the parameter for odd k up to the second order term. This extends previous results for complete binary trees.