Advanced search

Browse by subject

Browse by provider

Browse by language

Content Details
Normal View
CIP View

Disproof of a conjecture by Erd\H{o}s an...

Yang, Yuansheng...

Free

Share this content

Disproof of a conjecture by Erd\H{o}s and Guy on the crossing number of hypercubes by Yang, Yuansheng ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	02-08-2023
Summary	Let $Q_n$ be the $n$-dimensional hypercube, and let ${\rm cr}(Q_n)$ be the \textit{crossing number} of $Q_n$. Erd\H{o}s and Guy in 1973 conjectured the following equality: ${\rm cr}(Q_n)=\frac{5}{32}4^n-\lfloor\frac{n^2+1}{2}\rfloor 2^{n-2}$. In this paper, we construct a drawing of $Q_n$ with less crossings when $n>6$, which implies that for $n>6$ we have a strict inequality.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1201.4700

Citation

Review the full bibliography data and make any necessary corrections before using. Always consult your library resources for the exact formatting and punctuation guidelines.

AMA 11th EditionReferences

Yang, Yuansheng. Disproof of a conjecture by Erd\H{o}s and Guy on the crossing number of hypercubes. Australian National University. August 02, 2023. Accessed August 10, 2025. https://online.provdatabase.com/cite/9532

APA 7th EditionReferences

Yang, Yuansheng. (2023). Disproof of a conjecture by Erd\H{o}s and Guy on the crossing number of hypercubes. Australian National University. https://online.provdatabase.com/cite/9532

Chicago 17th EditionReferences

Yang, Yuansheng. Disproof of a conjecture by Erd\H{o}s and Guy on the crossing number of hypercubes. Australian National University. 2023. https://online.provdatabase.com/cite/9532

HarvardReferences

Yang, Yuansheng. (2023). Disproof of a conjecture by Erd\H{o}s and Guy on the crossing number of hypercubes. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/9532. (Accessed 10 August 2025).

Harvard AustraliaReferences

Yang, Yuansheng, 2023, Disproof of a conjecture by Erd\H{o}s and Guy on the crossing number of hypercubes, Australian National University, viewed 10 August 2025, <https://online.provdatabase.com/cite/9532>

MLA 9th EditionWorks Cited

Yang, Yuansheng. Disproof of a conjecture by Erd\H{o}s and Guy on the crossing number of hypercubes. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/9532.

Share this eBook