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Planar Graphs as VPG-Graphs
A graph is Bk-VPG when it has an intersection representation by paths in a rectangular grid with at most k bends (turns). It is known that all planar graphs are B3-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B2-VPG. We also show that the 4-connected planar graphs constitute a subclass of the intersection graphs of Z-shapes (i.e., a...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1933
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-21-1-73-84