Graphs with minimum fractional domatic number

Gadouleau, Maximilien, Harms, Nathaniel, Mertzios, George B and Zamaraev, Viktor ORCID: 0000-0001-5755-4141 (2024) Graphs with minimum fractional domatic number. Discrete Applied Mathematics, 343. pp. 140-148.

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Abstract

The domatic number of a graph is the maximum number of vertex disjoint dominating sets that partition the vertex set of the graph. In this paper we consider the fractional variant of this notion. Graphs with fractional domatic number 1 are exactly the graphs that contain an isolated vertex. Furthermore, it is known that all other graphs have fractional domatic number at least 2. In this note we characterize graphs with fractional domatic number 2. More specifically, we show that a graph without isolated vertices has fractional domatic number 2 if and only if it has a vertex of degree 1 or a connected component isomorphic to a 4-cycle. We conjecture that if the fractional domatic number is more than 2, then it is at least 7/3.

Item Type:	Article
Additional Information:	Source info: DA15620
Uncontrolled Keywords:	domination number, domatic number, fractional domatic number
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	03 Nov 2023 16:38
Last Modified:	10 Jan 2024 21:19
DOI:	10.1016/j.dam.2023.10.020
Open Access URL:	https://arxiv.org/abs/2302.11668
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3176546