• Bulletin of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1397-1404
• /
• 2018

For a connected graph G, an r-maximum edge-coloring is an edge-coloring f defined on E(G) such that at every vertex v with $d_G(v){\geq}r$ exactly r incident edges to v receive the maximum color. The r-maximum index $x^{\prime}_r(G)$ is the least number of required colors to have an r-maximum edge coloring of G. In this paper, we show how the r-maximum index is affected by adding an edge or a vertex. As a main result, we show that for each $r{\geq}3$ the r-maximum index function over the graphs admitting an r-maximum edge-coloring is unbounded and the range is the set of natural numbers. In other words, for each $r{\geq}3$ and $k{\geq}1$ there is a family of graphs G(r, k) with $x^{\prime}_r(G(r,k))=k$. Also, we construct a family of graphs not admitting an r-maximum edge-coloring with arbitrary maximum degrees: for any fixed $r{\geq}3$, there is an infinite family of graphs ${\mathcal{F}}_r=\{G_k:k{\geq}r+1\}$, where for each $k{\geq}r+1$ there is no r-maximum edge-coloring of $G_k$ and ${\Delta}(G_k)=k$.

• Journal of the Korean Mathematical Society
• /
• v.48 no.1
• /
• pp.105-115
• /
• 2011

Let f be a function which assigns a positive integer f(v) to each vertex v $\in$ V (G), let r, s and t be non-negative integers. An f-coloring of G is an edge-coloring of G such that each vertex v $\in$ V (G) has at most f(v) incident edges colored with the same color. The minimum number of colors needed to f-color G is called the f-chromatic index of G and denoted by ${\chi}'_f$(G). An [r, s, t; f]-coloring of a graph G is a mapping c from V(G) $\bigcup$ E(G) to the color set C = {0, 1, $\ldots$; k - 1} such that |c($v_i$) - c($v_j$ )| $\geq$ r for every two adjacent vertices $v_i$ and $v_j$, |c($e_i$ - c($e_j$)| $\geq$ s and ${\alpha}(v_i)$ $\leq$ f($v_i$) for all $v_i$ $\in$ V (G), ${\alpha}$ $\in$ C where ${\alpha}(v_i)$ denotes the number of ${\alpha}$-edges incident with the vertex $v_i$ and $e_i$, $e_j$ are edges which are incident with $v_i$ but colored with different colors, |c($e_i$)-c($v_j$)| $\geq$ t for all pairs of incident vertices and edges. The minimum k such that G has an [r, s, t; f]-coloring with k colors is defined as the [r, s, t; f]-chromatic number and denoted by ${\chi}_{r,s,t;f}$ (G). In this paper, we present some general bounds for [r, s, t; f]-coloring firstly. After that, we obtain some important properties under the restriction min{r, s, t} = 0 or min{r, s, t} = 1. Finally, we present some problems for further research.

• Journal of Technologic Dentistry
• /
• v.36 no.4
• /
• pp.247-253
• /
• 2014

Purpose: The aim of this study was to evaluate the effect of colored zirconia with different coloring liquids. Methods: Total 30 specimens were prepared. Specimens were classified into 6 groups: IPS e.max Ceram(P), Uncolored zirconia(C), VITA In-Ceram$^{(R)}$2000 YZ LL1(L), Zirkonzahn coloring liquid(Z), Wieland coloring liquid(W), and Kuwotech coloring liquid(K). Four different types of zirconia coloring liquid, VITA In-Ceram$^{(R)}$ 2000 YZ LL1(VITA Zahnfabrik, Germany), Zirkonzahn coloring liquid(Zirkonzahn, Italy), Wieland coloring liquid(Wieland, Germany), Kuwotech coloring liquid(Kuwotech, Korea) were used to fabricate colored zirconia by using infiltrating method and then completely sintered. The color of the all specimens was measured using the spectrophotometer(CM-2600d, Konica Minolta, Japan) and expressed in terms of the 3-coordinated values(CIE $L^*a^*b^*$). Color differences were calculated using the equation $${\Delta}E^*=[({\Delta}L^*)^2+({\Delta}a^*)^2+({\Delta}b^*)^2]^{1/2}$$. Results: $L^*a^*b^*$ values of the colored zirconia were affected by the coloring liquids. The uncolored zirconia(C) group showed the highest $L^*$ value and zirkonzahn coloring liquid(Z) group showed the lowest $L^*$ value. Zirkonzahn coloring liquid(Z) showed the highest $a^*$ value and VITA In-Ceram 2000 YZ LL1(L) group showed the highest $b^*$ value. Generally, the color difference(${\Delta}E^*$) in all groups showed higher than 3.7 except between IPS e.max Ceram(P) and wieland coloring liquid(W) group. Conclusion: Within the limitations of this study, various coloring liquids influenced the $L^*$, $a^*$, and $b^*$ values of colored zirconia. IPS e.max Ceram(P) and wieland coloring liquid(W) group did not show clinically perceiving color difference.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.909-913
• /
• 2009

For a family of graphs $\mathcal{H}$ and an integer k, we denote by $R^k(\mathcal{H})$ the corresponding k-Ramsey number, which is defined to be the smallest integer n such that every k-coloring of the edges of $K_n$ contains a monochromatic copy of a graph in $\mathcal{H}$. The local k-Ramsey number $R^k_{loc}(\mathcal{H})$ and the mean k-Ramsey number $R^k_{mean}(\mathcal{H})$ are defined analogously. Let $\mathcal{G}$ be the family of non-bipartite graphs and $T_n$ be the family of all trees on n vertices. In this paper we prove that $R^k_{loc}(\mathcal{G})=R^k_{mean}(\mathcal{G})$, and $R^2(T_n)$ < $R^2_{loc}(T_n)4 = $R^2_{mean}(T_n)$ for all $n\;{\ge}\;3$.

• Journal of the Korean Society of Fashion and Beauty
• /
• v.3 no.1 s.4
• /
• pp.72-77
• /
• 2005

The present study was to investigate the effects of different types of conditioner on the morphological changes of hair cuticles after coloring treatment. The virgin hair, aged 22 years served as a subject. Coloring treatment was done with a commercial hair dye agent for 35 minutes as routine procedures at $25^{\circ}C$, 50% R.H. environmental condition. The two different types of conditioner, Essence and LPP were applied to the colored hair 10 times with 2 days interval for 20 days. The hair cuticles were observed by a scanning electron micro scopy before and after coloring and conditioner treatment. The main results were as follows. Coloring treatment damaged the hair cuticles, and both of Essence and LPP had a direct conditioning effect. Also, the damaged hair cuticles were recovered by the repeated application of hair conditioner. Moreover, LPP was more effective in hair curing compared to Essence. These results show that a hair conditioner can be helpful to keep healthy hair and to shorten an interval of coloring.

• Korean Journal of Mathematics
• /
• v.28 no.2
• /
• pp.379-389
• /
• 2020

An r-color Rado number N = R(𝓛, r) for a system 𝓛 of equations is the least integer, provided it exists, such that for every r-coloring of the set {1, 2, …, N}, there is a monochromatic solution to 𝓛. In this paper, we study the 2-color Rado number R(𝓔, 2) for 𝓔 : x₁ + x₂ + ⋯ + x_n = y₁ + y₂ = z when n ≥ 4.

• Culinary science and hospitality research
• /
• v.8 no.2
• /
• pp.153-171
• /
• 2002

This study had three major purpose: 1) to examine the relationship between coloring factor of Hors d'oeuvre and preference of dishes. 2) to examine the relationship between coloring factor of Hors d'oeuvre and selection of dishes. 3) to examine the relationship between coloring factor of Hors d'oeuvre and customer satisfaction. Questionnaires for the study were distributed 300 subjects in deluxe class hotels in Seoul. Among 300 questionnaires, 280 subjects were collected and utilized for analysis. In HY hotel, 35 subjects of customers, 24 subjects of cooks, and 32 subjects of service personnels were collected. In R hotel, 29 subjects of customers, 32 subjects of cooks, and 32 subjects of service personnels were collected. In H hotel, 29 subjects of customers, 34 subjects of cooks, and 33 subjects of service personnels were collected. Analysis ways used for this study were frequency analysis, factor analysis, reliability analysis, ANOVA, To accomplished the objective 1), ANOVA was utilized. To accomplished the objective 2) and 3), regression analysis was unitized. The findings from this study were as follows. First it was found that selection of dishes was affected by coloring factory of Hors d'oeuvre. Secondly, it was found that customer satisfaction was affected by coloring factor of Hors d'oeuvre. Consequently, development of Hors d'oeuvre by harmonizing of various colorings should be activated to raise level of preference of dishes. Also, in regard to level of satisfaction, harmony of various colorings should be required.

• Journal of Environmental Science International
• /
• v.14 no.12
• /
• pp.1195-1201
• /
• 2005

In order to develop a dye coloring technology on Conchiolin layer in cultured pearls, appropriate dyes were selected, their solubilities in various solvents were studied, and adsorption and desorption experiments were performed. Solubilities of several basic dyes known to suitable for the pearl coloring, i.e., Rhodamine 6G(R6), Rhodamine B(RB) and Methylene Blue(MB), in several solvents (distilled water, methanol, ethanol, and acetone) were investigated. Among these dyes, R6 was chosen as a dye for single component adsorption and desorption experiment due to the relatively good solubility in various solvents tested. Solubilities of dyes were judged to be enough to color the pearls since dye concentrations in pearl coloring are, in general, not so high. The internal surface area of the pearl layer is believed to be directly related to the dye adsorption, the single-point internal surface area of the pearl layer measured at the nitrogen relative pressure of 0.3 was found to be $0.913m^2/g$, and the BET internal surface area, $1.01m^2/g$ The most probable diameters of micropores and macropores were found to be $40{\AA}$and $5000{\AA}$ respectively, from the pore size distribution data. Adsorption isotherm was well fitted to the Langmuir isotherm model, resulting in q=$\frac{1.62C}{1+1.09C^{.}}$

• The KIPS Transactions:PartB
• /
• v.11B no.2
• /
• pp.221-226
• /
• 2004

Ant Colony System(ACS) Algorithm is new meta-heuristic for hard combinational optimization problem. It is a population-based approach that uses exploitation of positive feedback as well as greedy search. Recently, various methods and solutions are proposed to solve optimal solution of graph coloring problem that assign to color for adjacency node($v_i, v_j$) that they has not same color. In this paper introducing ANTCOL Algorithm that is method to solve solution by Ant Colony System algorithm that is not method that it is known well as solution of existent graph coloring problem. After introducing ACS algorithm and Assignment Type Problem, show the wav how to apply ACS to solve ATP And compare graph coloring result and execution time when use existent generating functions(ANT_Random, ANT_LF, ANT_SL, ANT_DSATUR, ANT_RLF method) with ANT_XRLF method that use XRLF that apply Randomize to RLF to solve ANTCOL. Also compare graph coloring result and execution time when use method to add re-search to ANT_XRLF(ANT_XRLF_R) with existent generating functions.

• Analytical Science and Technology
• /
• v.26 no.1
• /
• pp.99-105
• /
• 2013

To identify oxidative hair dyes in hair-coloring products, the thin-layer chromatography (TLC) screening method was used in accordance with Korean Quasi-drug Codex. However, the TLC method is not reliable when there are very small amount of materials to be tested or when $R_f$ values of several components are similar. In this study, Ultra Performance Liquid Chromatography (UPLC) with a rapid sample preparation method was developed for the reliable and sensitive identification of active components contained in oxidative hair-coloring products. Hexane-distilled water was used for the extraction of active components contained in the products prior to UPLC analysis. The limit of detection of active components was 6.7-77.9 ${\mu}g/L$, and the limit of quantitation was 22.3-259.7 ${\mu}g/L$. Except for ${\alpha}$-naphthol, the range of recovery ratio was 96.2-101.5%. From this study, we demonstrated that oxidative active hair-coloring components can easily be analyzed by rapid extraction method followed by UPLC analysis.