Linear Layouts of Complete Graphs

Felsner, Stefan; Merker, Laura; Ueckerdt, Torsten; Valtr, Pável

doi:10.1007/978-3-030-92931-2_19

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…The most prominent types of linear layouts are stack layouts (no two edges of the same part cross) and queue layouts (no two edges of the same part nest, i.e., two edges ab and cd ordered a ≺ c ≺ d ≺ b are forbidden) [32,28,17]. These are accompanied by a rich field of further variants like mixed layouts (a combination of stack and queue layouts) [32,44,4], track layouts [18,5,45], local variants thereof [40,39,20,4] and more [19].…”

Section: Related Workmentioning

confidence: 99%

Directed Acyclic Outerplanar Graphs Have Constant Stack Number

Jungeblut¹,

Merker²,

Ueckerdt³

2022

Preprint

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The stack number of a directed acyclic graph G is the minimum k for which there is a topological ordering of G and a k-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering. We prove that the stack number of directed acyclic outerplanar graphs is bounded by a constant, which gives a positive answer to a conjecture by Heath, Pemmaraju and Trenk [SIAM J. Computing, 1999]. As an immediate consequence, this shows that all upward outerplanar graphs have constant stack number, answering a question by Bhore et al. [GD 2021] and thereby making significant progress towards the problem for general upward planar graphs originating from Nowakowski and Parker [Order, 1989]. As our main tool we develop the novel technique of directed H-partitions, which might be of independent interest.We complement the bounded stack number for directed acyclic outerplanar graphs by constructing a family of directed acyclic 2-trees that have unbounded stack number, thereby refuting a conjecture by Pupyrev [arXiv:2107.13658, 2021].

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