A note on packing chromatic number of the square lattice.

Soukal, Roman; Holub, Přemysl

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Displaying similar documents to “A note on packing chromatic number of the square lattice.”

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

Yolandé Jacobs, Elizabeth Jonck, Ernst Joubert (2013)

Open Mathematics

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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...

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Kelmans, Alexander, Mubayi, Dhruv, Sudakov, Benny (2001)

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Packing the Hypercube

David Offner (2014)

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Let G be a graph that is a subgraph of some n-dimensional hypercube Qn. For sufficiently large n, Stout [20] proved that it is possible to pack vertex- disjoint copies of G in Qn so that any proportion r < 1 of the vertices of Qn are covered by the packing. We prove an analogous theorem for edge-disjoint packings: For sufficiently large n, it is possible to pack edge-disjoint copies of G in Qn so that any proportion r < 1 of the edges of Qn are covered by the packing.

A Note on Uniquely Embeddable Forests

Justyna Otfinowska, Mariusz Woźniak (2013)

Discussiones Mathematicae Graph Theory

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Let F be a forest of order n. It is well known that if F 6= Sn, a star of order n, then there exists an embedding of F into its complement F. In this note we consider a problem concerning the uniqueness of such an embedding.

Algorithms for investigating optimality of cone triangulation for a polyhedron

Milica Stojanović, Milica Vučković (2007)

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Packing Coloring of Some Undirected and Oriented Coronae Graphs

Daouya Laïche, Isma Bouchemakh, Éric Sopena (2017)

Discussiones Mathematicae Graph Theory

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The packing chromatic number χρ(G) of a graph G is the smallest integer k such that its set of vertices V(G) can be partitioned into k disjoint subsets V1, . . . , Vk, in such a way that every two distinct vertices in Vi are at distance greater than i in G for every i, 1 ≤ i ≤ k. For a given integer p ≥ 1, the p-corona of a graph G is the graph obtained from G by adding p degree-one neighbors to every vertex of G. In this paper, we determine the packing chromatic number of p-coronae...