The number of edges of the edge polytope of a finite simple graph
| Autor: | Hibi, Takayuki, Mori, Aki, Ohsugi, Hidefumi, Shikama, Akihiro |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | ARS Mathematica Contemporanea 10 (2016) 323-332 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.26493/1855-3974.722.bba |
| Popis: | Let $d \geq 3$ be an integer. It is known that the number of edges of the edge polytope of the complete graph with $d$ vertices is $d(d-1)(d-2)/2$. In this paper, we study the maximum possible number $\mu_d$ of edges of the edge polytope arising from finite simple graphs with $d$ vertices. We show that $\mu_{d}=d(d-1)(d-2)/2$ if and only if $3 \leq d \leq 14$. In addition, we study the asymptotic behavior of $\mu_d$. Tran--Ziegler gave a lower bound for $\mu_d$ by constructing a random graph. We succeeded in improving this bound by constructing both a non-random graph and a random graph whose complement is bipartite. Comment: 10 pages, V2: Major Revision (We replace Section 2 with the results on the asymptotic behavior of $\mu_d$), V3-V4: The writing is improved |
| Databáze: | arXiv |
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