تقرير
Nordhaus-Gaddum inequalities for the number of cliques in a graph
| العنوان: | Nordhaus-Gaddum inequalities for the number of cliques in a graph |
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| المؤلفون: | Bal, Deepak, Cutler, Jonathan, Pebody, Luke |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | Nordhaus and Gaddum proved sharp upper and lower bounds on the sum and product of the chromatic number of a graph and its complement. Over the years, similar inequalities have been shown for a plenitude of different graph invariants. In this paper, we consider such inequalities for the number of cliques (complete subgraphs) in a graph $G$, denoted $k(G)$. We note that some such inequalities have been well-studied, e.g., lower bounds on $k(G)+k(\overline{G})=k(G)+i(G)$, where $i(G)$ is the number of independent subsets of $G$, has been come to be known as the study of Ramsey multiplicity. We give a history of such problems. One could consider fixed sized versions of these problems as well. We also investigate multicolor versions of these problems, meaning we $r$-color the edges of $K_n$ yielding graphs $G_1,G_2,\ldots,G_r$ and give bounds on $\sum k(G_i)$ and $\prod k(G_i)$. Comment: 15 pages, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.03355 |
| رقم الأكسشن: | edsarx.2406.03355 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |