The packing chromatic number of the square lattice is at least 12
نویسندگان
چکیده
The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set V (G) can be partitioned into disjoint classes X1, . . . , Xk, where vertices in Xi have pairwise distance greater than i. For the 2-dimensional square lattice Z it is proved that χρ(Z ) ≥ 12, which improves the previously known lower bound 10.
منابع مشابه
A Note on Packing Chromatic Number of the Square Lattice
The concept of a packing colouring is related to a frequency assignment problem. The packing chromatic number χp(G) of a graph G is the smallest integer k such that the vertex set V (G) can be partitioned into disjoint classes X1, . . . , Xk, where vertices in Xi have pairwise distance greater than i. In this note we improve the upper bound on the packing chromatic number of the square lattice.
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عنوان ژورنال:
- CoRR
دوره abs/1003.2291 شماره
صفحات -
تاریخ انتشار 2010