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Balanced k-Colorings
[chapter]

2000
*
Lecture Notes in Computer Science
*

While discrepancy theory is normally only studied in the context of 2-

doi:10.1007/3-540-44612-5_16
fatcat:nzwdbvwhrrebfmnl3ot44tm7gu
*colorings*, we explore the problem of*k*-*coloring*, for*k*¿ 2, a set of vertices to minimize imbalance among a family of subsets of vertices ... For 2-*colorings*, the bound on the discrepancy is atmost max{2d − 3; 2}. Finally, we prove that several restricted versions of computing the discrepancy are NP-complete. (E.D. ... Theorem 1 (*Balance*Theorem). Let d¿2 and*k*¿2. Let L be a set of lines of dimension d containing a set of vertices P. Then P has a (4d−3)-*balanced**k*-*coloring*. ...##
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Balanced k-colorings

2002
*
Discrete Mathematics
*

While discrepancy theory is normally only studied in the context of 2-

doi:10.1016/s0012-365x(01)00431-9
fatcat:dhkuh34ra5hjtntflw6vakamzm
*colorings*, we explore the problem of*k*-*coloring*, for*k*¿ 2, a set of vertices to minimize imbalance among a family of subsets of vertices ... For 2-*colorings*, the bound on the discrepancy is atmost max{2d − 3; 2}. Finally, we prove that several restricted versions of computing the discrepancy are NP-complete. (E.D. ... Theorem 1 (*Balance*Theorem). Let d¿2 and*k*¿2. Let L be a set of lines of dimension d containing a set of vertices P. Then P has a (4d−3)-*balanced**k*-*coloring*. ...##
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Colorings of k-balanced matrices and integer decomposition property of related polyhedra

2007
*
Operations Research Letters
*

This is accomplished by proving certain

doi:10.1016/j.orl.2006.06.006
fatcat:utmkypqk2zdslhcvxnhtyvdmaq
*coloring*properties of these matrices. ... This concept is related to that of*k*-*balancedness*as follows. ... The proof of Theorem 1 will follow from certain*coloring*properties of the class of*k*-*balanced*matrices, that we present in the next section. ...##
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Parallel Heuristics for Improved, Balanced Graph Colorings

1996
*
Journal of Parallel and Distributed Computing
*

In the second part of the paper we introduce two new parallel

doi:10.1006/jpdc.1996.0117
fatcat:r7c3m2wymzaofhbknk3gyfl4me
*color*-*balancing*heuristics, PDR(*k*) and PLF(*k*). ... We show that these heuristics have the desirable property that they do not increase the number of*colors*used by an initial*coloring*during the*balancing*process. ... To achieve the second objective,*balanced**colorings*, we introduced the the PLF(*k*) and PDR(*k*) heuristics. ...##
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Performance of the Caltech Submillimeter Observatory Dual-Color 180–720 GHz Balanced SIS Receivers

2014
*
IEEE Transactions on Terahertz Science and Technology
*

We report on

doi:10.1109/tthz.2013.2293117
fatcat:6xbdguulmvf73fprphc7pu3mw4
*balanced*SIS receivers covering the astronomical important 180-720 GHz submillimeter atmospheric window. ... Instrumental stability is excellent supporting the LO noise cancellation properties of the*balanced*mixer configuration. ... Zmuidzinas of the California Institute of Technology for providing the*K*a -band synthesizers, the wideband Fast Fourier Transform Spectrometers (FFTS), and for his advise and physics insight over the ...##
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Brightness, Contrast, and Color Balance of Digital versus Film Retinal Images in the Age-Related Eye Disease Study 2

2008
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Investigative Ophthalmology and Visual Science
*

Image brightness (B), contrast (C), and

doi:10.1167/iovs.07-1267
pmid:18421079
fatcat:jqntjpidvneo3fw4lqk4airhau
*color**balance*(CB) were measured with three-*color*luminance histograms. ... Exemplar images had similar brightness, contrast, and*color**balance*, supporting an image model. ... temperature, 6300°*K*) from the original AREDS. ...##
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Balanced k-decompositions of graphs

2012
*
Discrete Applied Mathematics
*

For a given integer

doi:10.1016/j.dam.2012.02.029
fatcat:ogixflcbqraktbvbs2agp3bfhe
*k*≥ 2, a*balanced**k*-*coloring*of a graph G is a mapping c: In this paper, we determine f*k*(G) for some graphs of high connectivity, trees and complete multipartite graphs. ... Consider a*balanced**k*-*coloring*c of G that*colors*tm + 1 vertices of S 1 by i for each*color*i from 1 to*k*, and leaves the other vertices uncolored. ... In all the above cases, we can choose the other*k*− 3*color*classes A 4 , A 5 , . . . , A*k*such that all leaves are*colored*. We claim that this*balanced**k*-*coloring*is optimal. ...##
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An Optimal Algorithm for Plane Matchings in Multipartite Geometric Graphs
[chapter]

2015
*
Lecture Notes in Computer Science
*

Given a

doi:10.1007/978-3-319-21840-3_6
fatcat:cphrsm346fhwpcovev7psjsabe
*color*-*balanced*point set P , a*balanced*cut is a line which partitions P into two colorbalanced point sets, each of size at most 2n/3+1. ... Let P be a set of n points in general position in the plane which is partitioned into*color*classes. P is said to be*color*-*balanced*if the number of points of each*color*is at most n/2 . ... Since P is*color*-*balanced*,*K*n (P 1 , . . . , P*k*) has Θ(n 2 ) edges. ...##
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An optimal algorithm for plane matchings in multipartite geometric graphs

2017
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Computational geometry
*

Given a

doi:10.1016/j.comgeo.2017.02.004
fatcat:fktko2gnqngv5hcy7zhrc26fmm
*color*-*balanced*point set P , a*balanced*cut is a line which partitions P into two colorbalanced point sets, each of size at most 2n/3+1. ... Let P be a set of n points in general position in the plane which is partitioned into*color*classes. P is said to be*color*-*balanced*if the number of points of each*color*is at most n/2 . ... Since P is*color*-*balanced*,*K*n (P 1 , . . . , P*k*) has Θ(n 2 ) edges. ...##
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Balanced Interval Coloring

2011
*
Symposium on Theoretical Aspects of Computer Science
*

This problem naturally models a load

doi:10.4230/lipics.stacs.2011.531
dblp:conf/stacs/AntoniadisHLMS11
fatcat:il6thvtc7bephjsemwvwbi6qlm
*balancing*scenario, where n tasks with given start-and endtimes have to be distributed among*k*servers. Our results imply that this can be done ideally*balanced*. ... We consider the discrepancy problem of*coloring*n intervals with*k**colors*such that at each point on the line, the maximal difference between the number of intervals of any two*colors*is minimal. ... any*k*∈ ◆, there is a*balanced**k*-*coloring*. ...##
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Balanced Interval Coloring
[article]

2010
*
arXiv
*
pre-print

This problem naturally models a load

arXiv:1012.3932v1
fatcat:pzpyaqrbarfc3bvzwdoqx5dgmq
*balancing*scenario, where n tasks with given start- and endtimes have to be distributed among*k*servers. Our results imply that this can be done ideally*balanced*. ... We consider the discrepancy problem of*coloring*n intervals with*k**colors*such that at each point on the line, the maximal difference between the number of intervals of any two*colors*is minimal. ... Existence of*Balanced**k*-*Colorings*We begin by observing the existence of*balanced**k*-*colorings*. ...##
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Good and nice colorings of balanced hypergraphs

2006
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Discrete Mathematics
*

Cornuejols, we show that oriented

doi:10.1016/j.disc.2005.12.044
fatcat:jkp4jh27ibewlercnr6jlfnanm
*balanced*hypergraphs have good*k*-*colorings*for any*k*. A stronger type of*coloring*is also shown to exist for oriented*balanced*hypergraphs. ... Berge who showed their existence in*balanced*hypergraphs. There is a simple generalization to oriented*balanced*hypergraphs: using the bi-*coloring*characterization of 0, ±1-matrices of M. ... . , S*k*) be a good*k*-*coloring*of an oriented*balanced*hypergraph H. ...##
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Balanced coloring of bipartite graphs

2009
*
Journal of Graph Theory
*

A

doi:10.1002/jgt.20456
fatcat:hnxykb2tyjg77mdmchow7zrnua
*balanced**coloring*of G is a*coloring*of the vertices of G such that each*color*class induces a*balanced*bipartite independent set in G. If graph G has a*balanced**coloring*we call it*colorable*. ... The*coloring*number χ B (G) is the minimum number of*colors*in a*balanced**coloring*of a*colorable*graph G. ... Given a*balanced*bipartite independent set I of size*k*in G r one can extend the r-partial*coloring*into a (r −*k*)-partial*coloring*in the following manner. ...##
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Colored unavoidable patterns and balanceable graphs
[article]

2021
*
arXiv
*
pre-print

We call an edge-

arXiv:1912.06302v3
fatcat:nqdqqhqq5vghxiivb66o4ibqy4
*coloring*of a path P_rk*balanced*if each*color*appears*k*times in the*coloring*. ... We show that any 3-edge-*coloring*of a large complete graph with kn+o(n) edges in each*color*contains a*balanced*P_3k. This is tight up to a constant factor of 2. ... Further, we say that an r-*coloring*of E(*K*n ) contains a*balanced*copy of G if it admits a*balanced*embedding of G. ...##
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Balance in Random Trees

2014
*
Open Journal of Discrete Mathematics
*

We prove that a random labeled (unlabeled) tree is

doi:10.4236/ojdm.2014.44013
fatcat:kpzr4vh4k5hnfpkrcjremhuwwy
*balanced*. We also prove that random labeled and unlabeled trees are strongly*k*-*balanced*for any 3*k*≥ . ... Edges with different*colored*endpoints are left uncolored. G is said to be*balanced*if neither the number of vertices nor and the number of edges of the two different*colors*differs by more than one. ... The map c will be called a*k*-*balanced**coloring*. Definition 1.5 Let 2*k*≥ . ...
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