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research article

Graphs with minimum fractional domatic number

Gadouleau, Maximilien
•
Harms, Nathaniel Idein  
•
Mertzios, George B.
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October 28, 2023
Discrete Applied Mathematics

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.(c) 2023 Published by Elsevier B.V.

  • Details
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Type
research article
DOI
10.1016/j.dam.2023.10.020
Web of Science ID

WOS:001102455400001

Author(s)
Gadouleau, Maximilien
•
Harms, Nathaniel Idein  
•
Mertzios, George B.
•
Zamaraev, Viktor
Date Issued

2023-10-28

Publisher

Elsevier

Published in
Discrete Applied Mathematics
Volume

343

Start page

140

End page

148

Subjects

Physical Sciences

•

Domination Number

•

Domatic Number

•

Fractional Domatic Number

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
THL5  
FunderGrant Number

NSERC MSFSS award

Available on Infoscience
February 19, 2024
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/204290
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