1. A Note on Packing Chromatic Number of the Square Lattice
- Author
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Pÿremysl Holub and Roman Soukal
- Subjects
Applied Mathematics ,Disjoint sets ,Frequency assignment problem ,Square lattice ,Upper and lower bounds ,Graph ,Theoretical Computer Science ,Vertex (geometry) ,Combinatorics ,Computational Theory and Mathematics ,Discrete Mathematics and Combinatorics ,Geometry and Topology ,Chromatic scale ,Mathematics - Abstract
The concept of a packing colouring is related to a frequency assignment problem. The packing chromatic number $\chi_p(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set $V (G)$ can be partitioned into disjoint classes $X_1, \dots, X_k$, where vertices in $X_i$ have pairwise distance greater than $i$. In this note we improve the upper bound on the packing chromatic number of the square lattice.
- Published
- 2010
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