scholarly journals On non-adaptive majority problems of large query size

2021 ◽  
Vol vol. 23, no. 3 (Analysis of Algorithms) ◽  
Author(s):  
Dániel Gerbner ◽  
Máté Vizer
Keyword(s):  
Color Class

We are given $n$ balls and an unknown coloring of them with two colors. Our goal is to find a ball that belongs to the larger color class, or show that the color classes have the same size. We can ask sets of $k$ balls as queries, and the problem has different variants, according to what the answers to the queries can be. These questions has attracted several researchers, but the focus of most research was the adaptive version, where queries are decided sequentially, after learning the answer to the previous query. Here we study the non-adaptive version, where all the queries have to be asked at the same time.

Strong Equitable Vertex Arboricity in Cartesian Product Networks

2021 ◽  
pp. 2150010
Author(s):  
Zhiwei Guo ◽  
Yaping Mao ◽  
Nan Jia ◽  
He Li
Keyword(s):  
Maximum Degree ◽  
Cartesian Product ◽  
Color Class ◽  
Vertex Arboricity

An equitable [Formula: see text]-tree-coloring of a graph [Formula: see text] is defined as a [Formula: see text]-coloring of vertices of [Formula: see text] such that each component of the subgraph induced by each color class is a tree of maximum degree at most [Formula: see text], and the sizes of any two color classes differ by at most one. The strong equitable vertex [Formula: see text]-arboricity of a graph [Formula: see text] refers to the smallest integer [Formula: see text] such that [Formula: see text] has an equitable [Formula: see text]-tree-coloring for every [Formula: see text]. In this paper, we investigate the Cartesian product with respect to the strong equitable vertex [Formula: see text]-arboricity, and demonstrate the usefulness of the proposed constructions by applying them to some instances of product networks.

Unsupervised color coding for visualizing image classification results

2017 ◽  
Vol 17 (2) ◽  
pp. 161-177 ◽  
Author(s):  
Simone Bianco ◽  
Raimondo Schettini
Keyword(s):  
Optimization Problems ◽  
General Purpose ◽  
Search Procedure ◽  
Color Coding ◽  
Class Label ◽  
Color Selection ◽  
Label Placement ◽  
Color Class ◽  
Local Search Procedure ◽  
Different Content

In this article, we describe a general purpose system that, given as input a segmented/classified image, automatically provides different visual outputs exploiting solid colors, color boundaries, and transparent colors. Moreover, if the names of the classes are given, the system automatically places a textual label in the less salient sub-region of the corresponding class. For color-class association and class label placement, we take into account the underlying image color and structure exploiting both saliency and superpixel representation. The color selection and the color-class association are formulated both as optimization problems and heuristically solved using a Local Search procedure. Results show the effectiveness of the proposed system on images having different content and different number of annotated regions.

scholarly journals Partitioning the Power Set of $[n]$ into $C_k$-free parts

10.37236/8385 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Eben Blaisdell ◽  
András Gyárfás ◽  
Robert A. Krueger ◽  
Ronen Wdowinski
Keyword(s):  
Upper Bound ◽  
Connected Graph ◽  
Type Problem ◽  
Color Class ◽  
Power Set ◽  
Ramsey Type ◽  
Partition Class ◽  
Cycle Path

We show that for $n \geq 3, n\ne 5$, in any partition of $\mathcal{P}(n)$, the set of all subsets of $[n]=\{1,2,\dots,n\}$, into $2^{n-2}-1$ parts, some part must contain a triangle — three different subsets $A,B,C\subseteq [n]$ such that $A\cap B,A\cap C,B\cap C$ have distinct representatives. This is sharp, since by placing two complementary pairs of sets into each partition class, we have a partition into $2^{n-2}$ triangle-free parts.  We also address a more general Ramsey-type problem: for a given graph $G$, find (estimate) $f(n,G)$, the smallest number of colors needed for a coloring of $\mathcal{P}(n)$, such that no color class contains a Berge-$G$ subhypergraph. We give an upper bound for $f(n,G)$ for any connected graph $G$ which is asymptotically sharp when $G$ is a cycle, path, or star. Additional bounds are given when $G$ is a $4$-cycle and when $G$ is a claw.

On strict strong coloring of graphs

2020 ◽  
pp. 2150040
Author(s):  
A. Mohammed Abid ◽  
T. R. Ramesh Rao
Keyword(s):  
Chromatic Number ◽  
Proper Coloring ◽  
Color Class ◽  
Minimum Number ◽  
Strong Chromatic Number

A strict strong coloring of a graph [Formula: see text] is a proper coloring of [Formula: see text] in which every vertex of the graph is adjacent to every vertex of some color class. The minimum number of colors required for a strict strong coloring of [Formula: see text] is called the strict strong chromatic number of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we characterize the results on strict strong coloring of Mycielskian graphs and iterated Mycielskian graphs.

scholarly journals New Concepts on Vertex and Edge Coloring of Simple Vague Graphs

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 373 ◽  
Author(s):  
Arindam Dey ◽  
Le Son ◽  
P. Kumar ◽  
Ganeshsree Selvachandran ◽  
Shio Quek
Keyword(s):  
Edge Coloring ◽  
Real Life ◽  
Review Of The Literature ◽  
Flow Management ◽  
Color Class ◽  
New Concepts ◽  
Traffic Flow Management ◽  
Vague Graph ◽  
Definition Of ◽  
Selection Of

The vague graph has found its importance as a closer approximation to real life situations. A review of the literature in this area reveals that the edge coloring problem for vague graphs has not been studied until now. Therefore, in this paper, we analyse the concept of vertex and edge coloring on simple vague graphs. Specifically, two new definitions for vague graphs related to the concept of the λ-strong-adjacent and ζ-strong-incident of vague graphs are introduced. We consider the color classes to analyze the coloring on the vertices in vague graphs. The proposed method illustrates the concept of coloring on vague graphs, using the definition of color class, which depends only on the truth membership function. Applications of the proposal in solving practical problems related to traffic flow management and the selection of advertisement spots are mainly discussed.

scholarly journals On the Separations of Common Proper Motion Binaries Containing White Dwarfs

1989 ◽  
Vol 114 ◽  
pp. 454-457
Author(s):  
T.D. Oswalt ◽  
E.M. Sion
Keyword(s):  
Mass Loss ◽  
White Dwarf ◽  
Proper Motion ◽  
White Dwarfs ◽  
Main Sequence ◽  
Late Type ◽  
Class A ◽  
Color Class

Luyten [1,2] and Giclas et al. [3,4] list over 500 known common proper motion binaries (CPMBs) which, on the basis of proper motion and estimated colors, are expected to contain at least one white dwarf (WD) component, usually paired with a late type main sequence (MS) star. Preliminary assessments of the CPMBs suggest that nearly all are physical pairs [5,6]. In this paper we address the issue of whether significant orbital expansion has occurred as a consequence of the post-MS mass loss expected to accompany the formation of the WDs in CPMBs.Though the CPMB sample remains largely unobserved, a spectroscopic survey of over three dozen CPMBs by Oswalt [5] found that nearly all faint components of Luyten and Giclas color class “a-f” and “+1”, respectively, or bluer were a WD. This tendency was also evident in a smaller sample studied by Greenstein [7]. Conversely, nearly all CPMBs having two components of color class “g-k” and “+3” or redder were MS+MS pairs. With the caveat that such criteria discriminate against CPMBs containing cool (but rare) WDs, they nonetheless provide a crude means of obtaining statistically significant samples for the comparison of orbital separations: 209 highly probable WD+MS pairs and 109 MS+MS pairs.

History and the West Indian nation

1998 ◽  
Vol 72 (3-4) ◽  
pp. 283-289
Author(s):  
Frank Birbalsingh
Keyword(s):  
New York ◽  
West Indies ◽  
West Indian ◽  
University Of Michigan ◽  
The West ◽  
Kamau Brathwaite ◽  
Color Class ◽  
Four Books ◽  
Ann Arbor ◽  
English Speaking

[First paragraph]The Art of Kamau Brathwaite. STEWART BROWN (ed.). Bridgend, Wales: Seren/Poetry Wales Press, 1995. 275 pp. (Cloth US$ 50.00, Paper US$ 22.95)Atlantic Passages: History, Community, and Language in the Fiction of Sam Selvon. MARK LOOKER. New York: Peter Lang, 1996. x + 243 pp. (Cloth n.p.)Caliban's Curse: George Lamming and the Revisioning of History. SUPRIYA NAIR. Ann Arbor: University of Michigan Press, 1996. viii + 171 pp. (Cloth US$ 34.50)Phyllis Shand Allfrey: A Caribbean Life. LlZABETH PARAVISINI-GEBERT. New Brunswick NJ: Rutgers University Press, 1996. xii + 335 pp. (Cloth US$ 55.00, Paper US$ 18.95)Of the four books to be considered here, those on Brathwaite, Selvon, and Lamming fit snugly together into a natural category of literature that has to do with the emergence of a Creole or African-centered Caribbean culture, and related issues of race, color, class, history, and nationality. The fourth is a biography of Phyllis Shand Allfrey, a white West Indian, who is of an altogether different race, color, and class than from the other three. Yet the four books are linked together by nationality, for Allfrey and the others are all citizens of one region, the English-speaking West Indies, which, as the Federation of the West Indies between 1958 and 1962, formed a single nation.

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