ALTERNATING HAMILTON CYCLES WITH MINIMUM NUMBER OF CROSSINGS IN THE PLANE
2000 ◽
Vol 10
(01)
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pp. 73-78
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Keyword(s):
Let X and Y be two disjoint sets of points in the plane such that |X|=|Y| and no three points of X ∪ Y are on the same line. Then we can draw an alternating Hamilton cycle on X∪Y in the plane which passes through alternately points of X and those of Y, whose edges are straight-line segments, and which contains at most |X|-1 crossings. Our proof gives an O(n2 log n) time algorithm for finding such an alternating Hamilton cycle, where n =|X|. Moreover we show that the above upper bound |X|-1 on crossing number is best possible for some configurations.
2017 ◽
Vol 27
(03)
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pp. 159-176
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2013 ◽
Vol 155
(1)
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pp. 173-179
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2018 ◽
Vol 27
(08)
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pp. 1850046
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2006 ◽
Vol 17
(05)
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pp. 1031-1060
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1997 ◽
Vol 07
(03)
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pp. 211-223
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Keyword(s):
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