Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A lower bound for the packing chromatic number of the Cartesian product of cycles

100%

Jacobs Y., Jonck E., Joubert E.

Open Mathematics

2013

tom 11

nr 7

1344-1357

Let G = (V, E) be a simple graph of order n and i be an integer with i ≥ 1. The set X i ⊆ V(G) is called an i-packing if each two distinct vertices in X i are more than i apart. A packing colouring of G is a partition X = {X 1, X 2, …, X k} of V(G) such that each colour class X i is an i-packing. The minimum order k of a packing colouring is called the packing chromatic number of G, denoted by χρ(G). In this paper we show, using a theoretical proof, that if q = 4t, for some integer t ≥ 3, then 9 ≤ χρ(C 4 □ C q). We will also show that if t is a multiple of four, then χρ(C 4 □ C q) = 9.

Ograniczanie wyników

1 Open Mathematics

1 Jacobs Y.

1 Jonck E.

1 Joubert E.

1 2013

Wyniki wyszukiwania

A lower bound for the packing chromatic number of the Cartesian product of cycles