Domination structure for number three
Misa Nakanishi
TL;DR
This paper investigates the domination number in cubic graphs and the structure of minimum dominating sets in 3-connected graphs, providing new conditions and structural insights related to Reed's conjecture.
Contribution
It offers a sufficient condition for Reed's conjecture in cubic graphs and characterizes the structure of minimum dominating sets in 3-connected graphs.
Findings
A new sufficient condition for Reed's conjecture in cubic graphs.
Structural description of minimum dominating sets involving cycles of length divisible by 3.
Insights into the domination number related to graph connectivity and cycle structure.
Abstract
From a research of several recent papers, in the first part, we are concerned with domination number in cubic graphs and give a sufficient condition of Reed's conjecture. In the second part, from a perspective, we study the structure of a minimum dominating set in 3-connected graphs. It is derived from a collection of cycles with length 0 mod 3.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra