Year: 2025
Type: article
Abstract: Since Reed conjectured in 1996 that the domination number of a connected cubic graph of order n is at most ⌈1/3n⌉, thedomination number of cubic graphs has been extensively studied. It is now known that the conjecture is false in general, but Henning and Dorbec showed that it holds for graphs with girth at least 9. Zhu and Wu stated an analogous conjecture for 2-connected cubic planar graphs. In this paper, we present a new upper bound for the domination number of subcubic planar graphs: if G is a subcubic planar graph with girth at least 8, then γ(G) < n₀ + 3/4 n₁ + 11/20 n₂ + 7/20 n₃, where ni denotes the number of vertices in G of degree i, for i ∈ {0, 1, 2, 3}. We also prove that if G is a subcubic planar graph with girth at least 9, then γ(G) < n₀ + 13/17 n₁ + 9/17 n₂ + 6/17 n₃.
Source: Ars Mathematica Contemporanea
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: Interplay of geometry, topology and algebra in structural and topological graph theory, Matchings, transversals, and hypergraphs, Graduate Research Workshops in Combinatorics, Graph theory, G5099342464, Metric Problems in Graphs and Hypergraphs, The game of Cops and Robber on graphs and geodesic spaces
OpenAlex ID: W4407189592