Independent domination, order, size, and maximum degree

Dantas, Simone; Henning, Michael A.; Arelis Baldeon Penao, Giovanna; Rautenbach, Dieter

doi:10.22049/cco.2025.30756.2609

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	Independent domination, order, size, and maximum degree
Communications in Combinatorics and Optimization
مقاله 2، دوره 11، شماره 4، اسفند 2026، صفحه 1073-1080 اصل مقاله (358.36 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2025.30756.2609
نویسندگان
Simone Dantas¹؛ Michael A. Henning²؛ Giovanna Arelis Baldeon Penao¹؛ Dieter Rautenbach^* ³
¹Instituto de Matemática e EstatÍstica, Universidade Federal Fluminense, Niterói, Brazil
²Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa
³Institute of Optimization and Operations Research, Ulm University, Ulm, Germany
چکیده
For a connected graph $G$ with $n>2\Delta$ vertices, $m$ edges, and maximum degree at most $\Delta\geq 3$, we show $i(G)\leq \left(1-\Omega\left(\frac{1}{\Delta^4}\right)\right)n-\frac{m}{\Delta}+O\left(\frac{1}{\Delta^2}\right)$ and discuss related problems.
کلیدواژه‌ها
independent domination؛ regular graph؛ bound

مراجع
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Independent domination, order, size, and maximum degree