• Journal of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1123-1137
• /
• 2015

We study colorings of regular trees using subball complexity b(n), which is the number of colored n-balls up to color-preserving isomorphisms. We show that for any k-regular tree, for k > 1, there are colorings of intermediate complexity. We then construct colorings of linear complexity b(n) = 2n + 2. We also construct colorings induced from sequences of linear subword complexity which has exponential subball complexity.

• Kyungpook Mathematical Journal
• /
• v.60 no.2
• /
• pp.349-359
• /
• 2020

We study perfect 2-colorings of regular graphs. In particular, we consider the 4-regular case. We obtain a characterization of perfect 2-colorings of toroidal grids.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.149-156
• /
• 2006

The circular list coloring is a circular version of list colorings of graphs. Let $\chi_{c,l}$ denote the circular choosability(or the circular list chromatic number). In this paper, the circular choosability of outer planar graphs and odd wheel is discussed.

• Korean Journal of Mathematics
• /
• v.27 no.2
• /
• pp.525-534
• /
• 2019

Let $P(G,{\lambda})$ denote the number of proper vertex colorings of G with ${\lambda}$ colors. The chromatic polynomial $P(C_n,{\lambda})$ for the cycle graph $C_n$ is well-known as $$P(C_n,{\lambda})=({\lambda}-1)^n+(-1)^n({\lambda}-1)$$ for all positive integers $n{\geq}1$. Also its inductive proof is widely well-known by the deletion-contraction recurrence. In this paper, we give this inductive proof again and three other proofs of this formula of the chromatic polynomial for the cycle graph $C_n$.

• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.913-924
• /
• 2023

We consider the number of colors for colorings of links by the symmetric group S₃ of degree 3. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by S₃ with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by S₃ with 5 colors, then the link also admits such a coloring with only 4 colors.

• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.359-365
• /
• 2012

Giving a planar graph G, let $x^'_l(G)$ and $x^{''}_l(G)$ denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if a planar graph G without 6-cycles with chord, then $x^'_l(G){\leq}{\Delta}(G)+1$ and $x^{''}_l(G){\leq}{\Delta}(G)+2$ where ${\Delta}(G){\geq}6$.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.511-517
• /
• 2008

Let G be a planar graph. It is proved that if G does not contain a k-cycle with a chord for some k ${\ni}$ {4,5,6}, then G is total-($\Delta(G)+2$)-colorable.

• Communications of the Korean Mathematical Society
• /
• v.30 no.1
• /
• pp.45-64
• /
• 2015

In this article, we consider a proper total coloring distinguishes adjacent vertices by sums, if every two adjacent vertices have different total sum of colors of the edges incident to the vertex and the color of the vertex. Pilsniak and Wozniak [15] first introduced this coloring and made a conjecture that the minimal number of colors need to have a proper total coloring distinguishes adjacent vertices by sums is less than or equal to the maximum degree plus 3. We study proper total colorings distinguishing adjacent vertices by sums of some graphs and their products. We prove that these graphs satisfy the conjecture.

• Journal of the Korean Society of Costume
• /
• v.50 no.5
• /
• pp.159-169
• /
• 2000

The purpose of this study Is to research the clothing and textiles recorded in Heikemonokatary which was written from 1131 to 1198. The research materials are 36 kinds of men's clothes and ornaments, 6 kinds of women's things, 10 kinds of colorings and 6 kinds of textiles. The results of this study are as follow : 1. There were many advanced warriors' clothes. Especially the helmets and armors were very gorgeous. The shapes of warriors' knives, arrows, shields were concretely described. The women's clothes were mostly unchanged from Nara period and Heian period. Women wore clothes on their heads when they went out. 2. One particular thing in color is that the brown color of that period was navy blue which is symbolic of victory. There were some textiles which was woven with the boiled silk thread in the latitude and the raw silk thread in the longitude. Besides, the blackening of teeth, the bobbed haler of boys, and the celebration of one's corning of age were described in the book.