Track Layouts, Layered Path Decompositions, and Leveled Planarity
نویسندگان
چکیده
منابع مشابه
Track Layouts, Layered Path Decompositions, and Leveled Planarity
We investigate two types of graph layouts, track layouts and layered path decompositions, and the relations between their associated parameters track-number and layered pathwidth. We use these two types of layouts to characterize leveled planar graphs, the graphs with planar layered drawings with no dummy vertices. It follows from the known NP-completeness of leveled planarity that track-number...
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A track graph is a graph with its vertex set partitioned into horizontal levels. It is track planar if there are permutations of the vertices on each level such that all edges can be drawn as weak monotone curves without crossings. The novelty and generalisation over level planar graphs is that horizontal edges connecting consecutive vertices on the same level are allowed. We show that track pl...
متن کاملTrack Layouts of Graphs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Figures . . . . . . . ....
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It is known that every proper minor-closed class of graphs has bounded stack-number (a.k.a. book thickness and page number). While this includes notable graph families such as planar graphs and graphs of bounded genus, many other graph families are not closed under taking minors. For fixed g and k, we show that every n-vertex graph that can be embedded on a surface of genus g with at most k cro...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2018
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-018-0487-5