$2$-limited broadcast domination in cubic graphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917286732890112 |
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| author | Choi, Myungho Park, Boram |
| author_facet | Choi, Myungho Park, Boram |
| contents | For a graph $G$, a function $f:V(G) \to \{0,1,2\}$ is called a $2$-limited dominating broadcast on $G$ if for every vertex $u$, there exists a vertex $v$ such that $f(v)>0$ and the distance between $u$ and $v$ in $G$ is at most $f(v)$. The {\it cost} of $f$ means the value $\sum_{v\in V(G)}f(v)$, and the {\it $2$-limited broadcast domination number} of $G$, denoted by $γ_{b,2}(G)$, is the cost of a $2$-limited dominating broadcast on $G$ with minimum cost. Henning, MacGillivray, and Yang (2020) conjectured that $γ_{b,2}(G)\leq \frac{|V(G)|}{3}$ for every cubic graph $G$. In this paper, we confirm the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19080 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $2$-limited broadcast domination in cubic graphs Choi, Myungho Park, Boram Combinatorics For a graph $G$, a function $f:V(G) \to \{0,1,2\}$ is called a $2$-limited dominating broadcast on $G$ if for every vertex $u$, there exists a vertex $v$ such that $f(v)>0$ and the distance between $u$ and $v$ in $G$ is at most $f(v)$. The {\it cost} of $f$ means the value $\sum_{v\in V(G)}f(v)$, and the {\it $2$-limited broadcast domination number} of $G$, denoted by $γ_{b,2}(G)$, is the cost of a $2$-limited dominating broadcast on $G$ with minimum cost. Henning, MacGillivray, and Yang (2020) conjectured that $γ_{b,2}(G)\leq \frac{|V(G)|}{3}$ for every cubic graph $G$. In this paper, we confirm the conjecture. |
| title | $2$-limited broadcast domination in cubic graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.19080 |