Abstract:A k-queue layout is a special type of a linear layout, in which the linear order avoids (k + 1)-rainbows, i.e., k + 1 independent edges that pairwise form a nested pair. The optimization goal is to determine the queue number of a graph, i.e., the minimum value of k for which a k-queue layout is feasible. Recently, Dujmović et al. [J. ACM, 67(4), 22:1-38, 2020] showed that the queue number of planar graphs is at most 49, thus settling in the positive a long-standing conjecture by Heath, Leighton and Rosenberg. … Show more
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