2024/12/28 by Dmitrii Taletskii, Taletskii, Dmitrii
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph theory and applications #Cellular Automata and Applications
paper · pdf · doi:10.48550/arxiv.2412.20120
The Gamma-Theta Conjecture states that if the domination number of a graph is equal to its eternal domination number, then it is also equal to its clique covering number. This conjecture is known to be true for several graph classes, such as outerplanar graphs, subcubic graphs and Ck-free graphs, where k ∈ \3,4\. In this paper, we prove the Conjecture for the class of planar graphs.