منابع مشابه
New bounds on a hypercube coloring problem
In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of χk̄(n), the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and uppe...
متن کاملNew Bounds on a Hypercube Coloring Problem and Linear Codes
In studying the scalability of optical networks, one problem arising involves coloring the vertices of the dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most are colored differently. Determining the exact value of , the minimum number of colors needed, appears to be a difficult problem. In this paper, we improve the known lower and ...
متن کاملA Radio Coloring of a Hypercube
A radio coloring of a graph G is an assignment of nonnegative integers to its nodes so that each pair of adjacent nodes have color numbers that differ by at least two, and any pair of nodes at distance 2 have different colors. Every graph has a radio coloring by simply assigning the odd integers 1, 3, 5, ......, but there is then a big difference between the smallest and largest colors. We defi...
متن کاملOn a list-coloring problem
We study the function f G de ned for a graph G as the smallest integer k such that the join ofG with a stable set of size k is not jV G j choosable This function was introduced recently in order to describe extremal graphs for a list coloring version of a famous inequality due to Nordhaus and Gaddum Some bounds and some exact values for f G are determined
متن کاملOn a Covering Problem in the Hypercube
In this paper, we address a particular variation of the Turán problem for the hypercube. Alon, Krech and Szabó (2007) asked “In an n-dimensional hypercube, Qn, and for ` < d < n, what is the size of a smallest set, S, of Q`’s so that every Qd contains at least one member of S?” Likewise, they asked a similar Ramsey type question: “What is the largest number of colors that we can use to color th...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2004
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2004.06.010