5 research outputs found
Cell-paths in mono- and bichromatic line arrangements in the plane
We show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and
no cell is revisited). When all lines have the same color, and hence the preceding alternating constraint is dropped, we prove that the dual graph of the arrangement always contains a path of length (n2).Peer ReviewedPostprint (author’s final draft
Cell-paths in mono- and bichromatic line arrangements in the plane
CombinatoricsWe prove that the dual graph of any arrangement of n lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of n red and blue lines — in general position and not all of the same color — there is a simple path through at least n cells where red and blue lines are crossed alternatingly
Cell-paths in mono- and bichromatic line arrangements in the plane
We show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and
no cell is revisited). When all lines have the same color, and hence the preceding alternating constraint is dropped, we prove that the dual graph of the arrangement always contains a path of length (n2).Peer Reviewe