Domination versus edge domination

Domination versus edge domination

We propose the conjecture that the domination number γ(G) of a Δ-regular graph G with Δ≥1 is always at most its edge domination number γe(G), which coincides with the domination number of its line graph. We prove that γ(G)≤1+2(Δ−1)Δ2Δγe(G) for general Δ≥1, and γ(G)≤76−1204γe(G) for Δ=3. Furthermore,...

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Veröffentlicht in:Discrete Applied Mathematics 2020-10, Vol.285, p.343-349
Hauptverfasser: Baste, Julien, Fürst, Maximilian, Henning, Michael A., Mohr, Elena, Rautenbach, Dieter
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science
Data Structures and Algorithms
Discrete Mathematics
Domination
Edge domination
Minimum maximal matching
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Beschreibung
Zusammenfassung:We propose the conjecture that the domination number γ(G) of a Δ-regular graph G with Δ≥1 is always at most its edge domination number γe(G), which coincides with the domination number of its line graph. We prove that γ(G)≤1+2(Δ−1)Δ2Δγe(G) for general Δ≥1, and γ(G)≤76−1204γe(G) for Δ=3. Furthermore, we verify our conjecture for cubic claw-free graphs.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2020.05.030