| Autor: |
Berkove, Ethan, Brilleslyper, Michael |
| Předmět: |
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| Zdroj: |
Integers: Electronic Journal of Combinatorial Number Theory; 2022, Vol. 22, p1-18, 18p |
| Abstrakt: |
Let Ank denote the set of k consecutive positive integers starting with n. The coprime graph associated to this set, G(Ank), is the graph whose vertices are elements of Ank and whose edges connect pairs of integers if and only if they are coprime. In this paper, we focus on complete subgraphs and complete bipartite subgraphs of G(Ank). We investigate how the sizes of these graphs change with n and k, and show that there are situations where there is no complete bipartite subgraph with k vertices. This happens precisely when Ank is a stapled sequence; we provide some numerical results on how frequently these occur. We also prove a result about the average size of the smaller bipartition of the most balanced bipartite subgraph. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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