Removing Even Crossings, Continued
نویسندگان
چکیده
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 allows the redrawing of a graph removing intersections on even edges remains true on highergenus surfaces. As a consequence, we can conclude that crS(G), the crossing number of the graph G on surface S, is bounded by 2 ocrS(G) , where ocr(G)S is the odd crossing number of G on surface S. Finally, we begin an investigation of optimal crossing configurations for which ocr = cr.
منابع مشابه
Removing Independently Even Crossings
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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