Graph coloring approach with new upper bounds for the chromatic number: team building application

2018 ◽  
Vol 52 (3) ◽  
pp. 807-818
Author(s):  
Assia Gueham ◽  
Anass Nagih ◽  
Hacene Ait Haddadene ◽  
Malek Masmoudi
Keyword(s):  
Chromatic Number ◽  
Graph Coloring ◽  
Upper Bound ◽  
Team Building ◽  
Upper Bounds ◽  
Real Case ◽  
Soft Constraints ◽  
Empirical Comparison ◽  
Hard And Soft Constraints

In this paper, we focus on the coloration approach and estimation of chromatic number. First, we propose an upper bound of the chromatic number based on the orientation algorithm described in previous studies. This upper bound is further improved by developing a novel coloration algorithm. Second, we make a theoretical and empirical comparison of our bounds with Brooks’s bound and Reed’s conjecture for class of triangle-free graphs. Third, we propose an adaptation of our algorithm to deal with the team building problem respecting several hard and soft constraints. Finally, a real case study from healthcare domain is considered for illustration.

Conflict-Free Colourings of Uniform Hypergraphs With Few Edges

2012 ◽  
Vol 21 (4) ◽  
pp. 611-622 ◽  
Author(s):  
A. KOSTOCHKA ◽  
M. KUMBHAT ◽  
T. ŁUCZAK
Keyword(s):  
Chromatic Number ◽  
Upper Bound ◽  
Upper Bounds ◽  
Uniform Hypergraph ◽  
Lower And Upper Bounds ◽  
Uniform Hypergraphs ◽  
Minimum Number

A colouring of the vertices of a hypergraph is called conflict-free if each edge e of contains a vertex whose colour does not repeat in e. The smallest number of colours required for such a colouring is called the conflict-free chromatic number of , and is denoted by χCF(). Pach and Tardos proved that for an (2r − 1)-uniform hypergraph with m edges, χCF() is at most of the order of rm1/r log m, for fixed r and large m. They also raised the question whether a similar upper bound holds for r-uniform hypergraphs. In this paper we show that this is not necessarily the case. Furthermore, we provide lower and upper bounds on the minimum number of edges of an r-uniform simple hypergraph that is not conflict-free k-colourable.

scholarly journals Improved Bounds for Radiok-Chromatic Number of HypercubeQn

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Laxman Saha ◽  
Pratima Panigrahi ◽  
Pawan Kumar
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Graph Coloring ◽  
Upper Bound ◽  
Channel Assignment ◽  
Assignment Problem ◽  
Communication Problem ◽  
Channel Assignment Problem

A number of graph coloring problems have their roots in a communication problem known as the channel assignment problem. The channel assignment problem is the problem of assigning channels (nonnegative integers) to the stations in an optimal way such that interference is avoided as reported by Hale (2005). Radiok-coloring of a graph is a special type of channel assignment problem. Kchikech et al. (2005) have given a lower and an upper bound for radiok-chromatic number of hypercubeQn, and an improvement of their lower bound was obtained by Kola and Panigrahi (2010). In this paper, we further improve Kola et al.'s lower bound as well as Kchikeck et al.'s upper bound. Also, our bounds agree for nearly antipodal number ofQnwhenn≡2(mod 4).

scholarly journals Another Approach to Non-Repetitive Colorings of Graphs of Bounded Degree

10.37236/9667 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Matthieu Rosenfeld
Keyword(s):  
Chromatic Number ◽  
Upper Bound ◽  
Upper Bounds ◽  
Maximal Degree ◽  
Chromatic Numbers ◽  
Compression Method ◽  
Bounded Degree ◽  
A Minor ◽  
Entropy Compression ◽  
Minor Improvement

We propose a new proof technique that applies to the same problems as the  Lovász Local Lemma or the entropy-compression method. We present this approach in the context of non-repetitive colorings and we use it to improve upper-bounds relating different non-repetitive chromatic numbers to the maximal degree of a graph. It seems that there should be other interesting applications of the presented approach. In terms of upper-bounds our approach seems to be as strong as entropy-compression, but the proofs are more elementary and shorter. The applications we provide in this paper are upper bounds for graphs of maximal degree at most $\Delta$: a minor improvement on the upper-bound of the non-repetitive chromatic number, a $4.25\Delta +o(\Delta)$ upper-bound on the weak total non-repetitive chromatic number, and a $ \Delta^2+\frac{3}{2^{1/3}}\Delta^{5/3}+ o(\Delta^{5/3})$ upper-bound on the total non-repetitive chromatic number of graphs. This last result implies the same upper-bound for the non-repetitive chromatic index of graphs, which improves the best known bound. 

Soft Skills among Students: A Case Study of UiTM Cawangan Kelantan

2019 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
Muhammad Faizal Samat ◽  
Norazlan Annual ◽  
Raznee Atisya Md Rashidi
Keyword(s):  
Problem Solving ◽  
Unemployment Rate ◽  
Significant Influence ◽  
Education System ◽  
Communication Skill ◽  
Soft Skills ◽  
Team Building ◽  
Leadership Skill ◽  
Quality In Education

This article contributes to ongoing debates about soft skills among students. In 2017, the unemployment rate in Malaysia was at 3.42 percent as compared to 2.85 percent in 2014. Education system must aim towards employability and ensure quality in education to reduce the percentage of unemployment. Thus, this study aims to investigate the development of soft skills among students through co-curriculum activities in UiTM Cawangan Kelantan. The sample were 113 students from UiTM Cawangan Kelantan. Questionnaires adapted from previous research to measure the communication skill, problem solving skill, team building skill, leadership skill and soft development of soft skills among students through co-curriculum activities. SEM-PLS 3.0 were employed in this study. The findings revealed only team building skill has significant influence on developments of soft skills among students through co-curriculum activities. However, the study indicates that communication skill, problem solving skill and leadership skill are not significant towards development of soft skills among students through cocurriculum activities.

scholarly journals Semantic and knowledge based support to business model evaluation to stimulate green behaviour of electric vehicles’ drivers and energy prosumers

2021 ◽  
Author(s):  
Beniamino Di Martino ◽  
Dario Branco ◽  
Luigi Colucci Cante ◽  
Salvatore Venticinque ◽  
Reinhard Scholten ◽  
...  
Keyword(s):  
Business Model ◽  
Model Evaluation ◽  
Business Models ◽  
Real Case ◽  
Sustainable Mobility ◽  
Semantic Framework ◽  
Knowledge Based ◽  
Survey Results ◽  
Energy Prosumers

AbstractThis paper proposes a semantic framework for Business Model evaluation and its application to a real case study in the context of smart energy and sustainable mobility. It presents an ontology based representation of an original business model and examples of inferential rules for knowledge extraction and automatic population of the ontology. The real case study belongs to the GreenCharge European Project, that in these last years is proposing some original business models to promote sustainable e-mobility plans. An original OWL Ontology contains all relevant Business Model concepts referring to GreenCharge’s domain, including a semantic description of TestCards, survey results and inferential rules.

scholarly journals AOX removal from pulp and paper wastewater by Fenton and photo-Fenton processes: A real case-study

2020 ◽  
Vol 6 ◽  
pp. 770-775 ◽  
Author(s):  
J.P. Ribeiro ◽  
C.C. Marques ◽  
I. Portugal ◽  
M.I. Nunes
Keyword(s):  
Pulp And Paper ◽  
Real Case ◽  
Paper Wastewater ◽  
Aox Removal
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