Disjoint Total Dominating Sets in Planar Graphs

Eva Rotenberg; Daniel Rutschmann; Carsten Thomassen

doi:10.1002/jgt.70032

Disjoint Total Dominating Sets in Planar Graphs

Eva Rotenberg
, Daniel Rutschmann^*
, Carsten Thomassen

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

The vertex set of any planar graph of minimum degree at least 3 can be colored in two colors so that every vertex has a neighbor of each color. If the graph is a planar triangulation, the coloring can be chosen such that every vertex has a neighbor of its own color and at least two neighbors of the opposite color.

Original language	English
Journal	Journal of Graph Theory
Number of pages	6
ISSN	0364-9024
DOIs	https://doi.org/10.1002/jgt.70032
Publication status	Accepted/In press - 2026

Keywords

Coupon coloring
Planar graphs
Total domatic number
Total domination

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10.1002/jgt.70032Licence: CC BY

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title = "Disjoint Total Dominating Sets in Planar Graphs",

abstract = "The vertex set of any planar graph of minimum degree at least 3 can be colored in two colors so that every vertex has a neighbor of each color. If the graph is a planar triangulation, the coloring can be chosen such that every vertex has a neighbor of its own color and at least two neighbors of the opposite color.",

keywords = "Coupon coloring, Planar graphs, Total domatic number, Total domination",

author = "Eva Rotenberg and Daniel Rutschmann and Carsten Thomassen",

year = "2026",

doi = "10.1002/jgt.70032",

language = "English",

journal = "Journal of Graph Theory",

issn = "0364-9024",

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T1 - Disjoint Total Dominating Sets in Planar Graphs

AU - Rotenberg, Eva

AU - Rutschmann, Daniel

AU - Thomassen, Carsten

PY - 2026

Y1 - 2026

N2 - The vertex set of any planar graph of minimum degree at least 3 can be colored in two colors so that every vertex has a neighbor of each color. If the graph is a planar triangulation, the coloring can be chosen such that every vertex has a neighbor of its own color and at least two neighbors of the opposite color.

AB - The vertex set of any planar graph of minimum degree at least 3 can be colored in two colors so that every vertex has a neighbor of each color. If the graph is a planar triangulation, the coloring can be chosen such that every vertex has a neighbor of its own color and at least two neighbors of the opposite color.

KW - Coupon coloring

KW - Planar graphs

KW - Total domatic number

KW - Total domination

U2 - 10.1002/jgt.70032

DO - 10.1002/jgt.70032

M3 - Journal article

SN - 0364-9024

JO - Journal of Graph Theory

JF - Journal of Graph Theory

ER -

Disjoint Total Dominating Sets in Planar Graphs

Abstract

Keywords

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