• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.105-115
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• 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 applied mathematics & informatics
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• v.42 no.3
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• pp.567-582
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• 2024

A total coloring of a graph G is an assignment of colors to the elements of a graphs G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G , denoted by χ''(G), is the minimum number of colors that suffice in a total coloring. In this paper, we proved the Behzad and Vizing conjecture for certain convex polytope graphs D^p_n, Q^p_n, R^p_n, E_n, S_n, G_n, T_n, U_n, C_n,respectively. This significant result in a graph G contributes to the advancement of graph theory and combinatorics by further confirming the conjecture's applicability to specific classes of graphs. The presented proof of the Behzad and Vizing conjecture for certain convex polytope graphs not only provides theoretical insights into the structural properties of graphs but also has practical implications. Overall, this paper contributes to the advancement of graph theory and combinatorics by confirming the validity of the Behzad and Vizing conjecture in a graph G and establishing its relevance to applied problems in sciences and engineering.

• Journal of the Korean Society of Costume
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• v.59 no.3
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• pp.109-130
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• 2009

This study examines the rotor characteristics of Guybang culture (women's living in Joseon) relics which the life images and mental world of women in Joseon if expressed to prepare rotor data to be utilized in modern design and information for color identity establishment of Korean women culture. The result of this study is as following: 1. From 176 pieces of relic photos, total of 1380 color chips were extracted. For color analysis, 1368 units (99.1%) of color data excluding achromatic 12 units (0.9%) among 1380 units of colors were used. With the standard of 10 color wheel of Munsell Color System, the result of studying distributions according to frequency, red was the highest by 25.9%, yellow was 21.4% in women's goods in Joseon period which the ratio of red and yellow was 473%. Other than that, GY 14.6%, YR 11.3% and RP 11.1% followed next which is studied that the warm colors that conveys enjoyable and glamorous feelings composed 84.3%; 2. As a result of tone analysis, high value low chroma ltg color showed highest distribution of 20% and d was 12.2%, b was 11.7% and sf was 8.8%. Generally, it showed high frequency in high value cocors such as ltg, sf and b of 40.5%t and in low chroma (ltg) and medium chroma (d, sf) of 41% and colors in bright and calm image was used the most. 3. As a result of analyzing relationship between hue & tone, the ltg tone of Y close to white in traditional color sensibility showed the highest frequency of 9.6% and ltg tone of GY(6.4%), b tone of RP(6.1%), and v(5.4%), b(5.4%), dp(5.3%) of R followed next. 4. As a result of analyzing the characteristics of coloring, it showed that in case of coloring contrasting hues, it is adjusted similar tones and in case of coloring less contrasting hue, the difference in tone is adjusted to be rather large to make harmonized coloring. Moreover, in case of coloring similar hues, the ratio of using same tone and similar tone was large which the coloring of calm image and dynamic image is all used.

• Journal of Fashion Business
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• v.16 no.1
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• pp.69-82
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• 2012

This thesis aimed to reduce the differences of hair color when hair coloring, so it researched the differences & changes in hair color before shampoo v.s. after shampoo and dry on different heat processes when acid hair color dyeing. Five hair color dyes (Y, R, B, G, Br) manufactured by two different corporations were used. The acid hair color dyes were tinted on black and bleached hair pieces subjected to 3 different heat process; 1. Normal Temperature($25^{\circ}C$, 30min.) / 2. Heating($40^{\circ}C$, 15min.)+Normal Temperature($25^{\circ}C$, 15min.) / 3. Heating($40^{\circ}C$, 30min.). Color numbers were divided by NCS value, chroma, and hue. Statistical averages were derived and t-test was conducted using SPSS V12. Hair color differences and changes were drawn on an NCS chart using Photo Shop PS. The conclu is; If acid hair colorings are separated by a heating process, hair value & chroma change before shampoo vs. after shampoo & dry regardless of the color of hair and the heat process. Hue is not changed or shifted counter clockwise NCS color circle, but some exceptions, and it's the same when the total heat process results are combined. Black hair's value shifted downward and chroma left, and hue stayed either neutral or one color or it shifted counter clockwise on NCS color circle. Bleached hair's value shifted upward and chroma right, and hue stayed one color or shifted counter clockwise, but some exceptions. And it can be shown on NCS chart.