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On Approximating the Achromatic Number
 SIAM Journal of Discrete Math
, 2001
"... The achromatic number problem is to legally color the vertices of an input graph with the maximum number of colors, denoted / ..."
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The achromatic number problem is to legally color the vertices of an input graph with the maximum number of colors, denoted /
Approximation Algorithms for the Achromatic Number
, 2001
"... INTRODUCTION A complete coloring of agY3fi G E# is a partition P =#V of the vertices V such that each induced subgedb #, V i P , is an independent set, and, for each pair of distinct sets V i #V j P , the induced subgub V j is not an independent set. Thelarg8W integW m for which ..."
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G has a completecoloring is called the achromatic number of thegebG and is denoted by ##G#. 404 01966774/01 $35.00 2001 Elsevier Science All rigWW reserved The achromatic number was defined and studied by Harary et al. [7] and Harary and Hedetniemi [6].Computing the achromatic number for agG8
On the achromatic number of the Cartesian product
 G 1 \Theta G
, 1992
"... ABSTRACT. We study the achromatic number of the Cartesian product of graphs G 1 and G 2 and obtain the following results: (i) maXl<t<rn min{l mn J, t(m + n 1) t 2 + I} t ~ w(Krn X Kn} if n>{m+n~> m = 2 or m n> 2; and 2n fl if n> m> 2. m 1 Moreover, for m 2,3, the bounds ..."
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ABSTRACT. We study the achromatic number of the Cartesian product of graphs G 1 and G 2 and obtain the following results: (i) maXl<t<rn min{l mn J, t(m + n 1) t 2 + I} t ~ w(Krn X Kn} if n>{m+n~> m = 2 or m n> 2; and 2n fl if n> m> 2. m 1 Moreover, for m 2
On the Achromatic Number of Hypercubes
, 1999
"... The achromatic number of a finite graph G, /(G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge. For an mdimensional hypercube P m 2 we prove: There exist constants 0 ! c 1 ! c 2 , independent of m, ..."
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The achromatic number of a finite graph G, /(G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge. For an mdimensional hypercube P m 2 we prove: There exist constants 0 ! c 1 ! c 2 , independent of m
Efficient approximation algorithms for the achromatic number
, 2006
"... The achromatic number problem is, given a graph G = (V, E), to find the greatest number of colors, Ψ(G), in a coloring of the vertices of G such that adjacent vertices get distinct colors and for every pair of colors some vertex of the first color and some vertex of the second color are adjacent. Th ..."
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The achromatic number problem is, given a graph G = (V, E), to find the greatest number of colors, Ψ(G), in a coloring of the vertices of G such that adjacent vertices get distinct colors and for every pair of colors some vertex of the first color and some vertex of the second color are adjacent
Bounds on the chromatic and achromatic numbers of complementary graphs
 in Recent Progress in Combinatorics
, 1969
"... In the present note, exact upper bounds on the sums of chromatic and achromatic numbers of complimentary graphs are determined Which prove in particular a conjecture by Hedetniemi (1966) and imply a bound due to Nordhaus and Gaddum (1956). ..."
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In the present note, exact upper bounds on the sums of chromatic and achromatic numbers of complimentary graphs are determined Which prove in particular a conjecture by Hedetniemi (1966) and imply a bound due to Nordhaus and Gaddum (1956).
An Approximation Algorithm for the Achromatic Number of Enhanced Hyper Petersen Networks
"... The achromatic number for a graph G = (V, E) is the largest integer m such that there is a partition of V into disjoint independent sets (V1,…,Vm) such that for each pair of distinct sets Vi, Vj, Vi ∪ Vj is not an independent set in G. In this paper we present an O(1)approximation algorithm to dete ..."
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The achromatic number for a graph G = (V, E) is the largest integer m such that there is a partition of V into disjoint independent sets (V1,…,Vm) such that for each pair of distinct sets Vi, Vj, Vi ∪ Vj is not an independent set in G. In this paper we present an O(1)approximation algorithm
Achromatic Number versus Pseudoachromatic Number: A Counterexample to a Conjecture of Hedetniemi
 Discrete Math
, 1998
"... The pseudoachromatic number of a graph is the largest number of colours in a (not necessarily proper) vertex colouring of the graph such that every pair of distinct colours appears on the endpoints of some edge. The achromatic number is largest number of colours which can be used if the colouring ..."
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The pseudoachromatic number of a graph is the largest number of colours in a (not necessarily proper) vertex colouring of the graph such that every pair of distinct colours appears on the endpoints of some edge. The achromatic number is largest number of colours which can be used
The JPEG still picture compression standard
 Communications of the ACM
, 1991
"... This paper is a revised version of an article by the same title and author which appeared in the April 1991 issue of Communications of the ACM. For the past few years, a joint ISO/CCITT committee known as JPEG (Joint Photographic Experts Group) has been working to establish the first international c ..."
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widely implemented JPEG method to date, and is sufficient in its own right for a large number of applications. This article provides an overview of the JPEG standard, and focuses in detail on the Baseline method. 1
Results 1  10
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