Labeling planar graphs with a condition at distance two
An $L(2,1)$-labeling of a graph is a mapping $c:V(G) \to \{0,\ldots,K\}$ such that the labels assigned to neighboring vertices differ by at least $2$ and the labels of vertices at distance two are different. Griggs and Yeh [SIAM J. Discrete Math. 5 (1992), 586―595] conjectured that every graph $G$ w...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2005-01-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3417/pdf |
| Summary: | An $L(2,1)$-labeling of a graph is a mapping $c:V(G) \to \{0,\ldots,K\}$ such that the labels assigned to neighboring vertices differ by at least $2$ and the labels of vertices at distance two are different. Griggs and Yeh [SIAM J. Discrete Math. 5 (1992), 586―595] conjectured that every graph $G$ with maximum degree $\Delta$ has an $L(2,1)$-labeling with $K \leq \Delta^2$. We verify the conjecture for planar graphs with maximum degree $\Delta \neq 3$. |
|---|---|
| ISSN: | 1365-8050 |