Since Reed conjectured in 1996 that the domination number of a connected cubic graph of order n is at most ?1/3n?, the domination 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 ?(G) < n0 + 3/4 n1 + 11/20 n2 + 7/20 n3, where n_i 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 ?(G) < n0 + 13/17 n1 + 9/17 n2 + 6/17 n3.

Rights

URN

URN:NBN:SI:DOC-5M5H6R3X

COBISSID

289327619

DOI

10.26493/1855-3974.3389.86c

Added

27.10.2026

Metadata

Citation

APA:

Cho, Eun-Kyung, Culver, Eric, Hartke, Stephen G., Iršič Chenoweth, Vesna (2026). Domination of subcubic planar graphs with large girth. Ars mathematica contemporanea, volume 26, issue 2, article p2.08, str. 1-32. URN:NBN:SI:DOC-5M5H6R3X from http://www.dlib.si

MLA:

Cho, Eun-Kyung, Culver, Eric, Hartke, Stephen G., Iršič Chenoweth, Vesna. "Domination of subcubic planar graphs with large girth." Ars mathematica contemporanea volume 26. issue 2. article p2.08 (2026) str. 1-32.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-5M5H6R3X>

Ars mathematica contemporanea
2008-
(Assembly record)