Removing even crossings on surfaces
نویسندگان
چکیده
منابع مشابه
Removing Even Crossings on Surfaces
We give a new, topological proof that the weak Hanani-Tutte theorem is true on orientable surfaces and extend the result to nonorientable surfaces. That is, we show that if a graph G cannot be embedded on a surface S, then any drawing of G on S must contain two edges that cross an odd number of times. We apply the result and proof techniques to obtain new and old results about generalized thrac...
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An edge in a drawing of a graph is called even if it intersects every other edge of the graph an even number of times. Pach and Tóth proved that a graph can always be redrawn such that its even edges are not involved in any intersections. We give a new, and significantly simpler, proof of a slightly stronger statement. We show two applications of this strengthened result: an easy proof of a the...
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We show that cr(G) ≤ (2 iocr(G) 2 ) settling an open problem of Pach and Tóth [5,1]. Moreover, iocr(G) = cr(G) if iocr(G) ≤ 2.
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In this paper we investigate how certain results related to the HananiTutte theorem can be lifted to orientable surfaces of higher genus. We give a new simple, geometric proof that the weak Hanani-Tutte theorem is true for higher-genus surfaces. We extend the proof to prove that bipartite generalized thrackles in a surface S can be embedded in S. We also show that a result of Pach and Tóth that...
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We determine the possible even sets of nodes on sextic surfaces in P, showing in particular that their cardinalities are exactly the numbers in the set {24, 32, 40, 56}. We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, of homological and computer algebra on the other. We give a ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2009
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2009.03.002