On rainbow domination of cubic graphs
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910364461957120 |
|---|---|
| author | Žerovnik, Janez |
| author_facet | Žerovnik, Janez |
| contents | The structure of minimal weight rainbow domination functions of cubic graphs are studied. Based on general observations for cubic graphs, generalized Petersen graphs $P(ck,k)$ are characterized whose 4- and 5-rainbow domination numbers equal the general lower bounds. As $t$-rainbow domination of cubic graphs for $t \ge 6$ is trivial, characterizations of such generalized Petersen graphs $P(ck,k)$ are known for all $t$-rainbow domination numbers.In addition, new upper bounds for 4- and 5-rainbow domination numbers that are valid for all $P(ck,k)$ are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07538 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On rainbow domination of cubic graphs Žerovnik, Janez Combinatorics 05Cxx G.2.2; F.2.2 The structure of minimal weight rainbow domination functions of cubic graphs are studied. Based on general observations for cubic graphs, generalized Petersen graphs $P(ck,k)$ are characterized whose 4- and 5-rainbow domination numbers equal the general lower bounds. As $t$-rainbow domination of cubic graphs for $t \ge 6$ is trivial, characterizations of such generalized Petersen graphs $P(ck,k)$ are known for all $t$-rainbow domination numbers.In addition, new upper bounds for 4- and 5-rainbow domination numbers that are valid for all $P(ck,k)$ are provided. |
| title | On rainbow domination of cubic graphs |
| topic | Combinatorics 05Cxx G.2.2; F.2.2 |
| url | https://arxiv.org/abs/2403.07538 |