• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.573-580
• /
• 2012

A (1, ${\lambda}$)-embedded graph is a graph that can be embedded on a surface with Euler characteristic ${\lambda}$ so that each edge is crossed by at most one other edge. A graph $G$ is called ${\alpha}$-linear if there exists an integral constant ${\beta}$ such that $e(G^{\prime}){\leq}{\alpha}v(G^{\prime})+{\beta}$ for each $G^{\prime}{\subseteq}G$. In this paper, it is shown that every (1, ${\lambda}$)-embedded graph $G$ is 4-linear for all possible ${\lambda}$, and is acyclicly edge-($3{\Delta}(G)+70$)-choosable for ${\lambda}$ = 1, 2.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.19 no.3
• /
• pp.193-199
• /
• 2019

In this paper I propose an algorithm of linear time complexity for NP-complete Maximum Independent Set (MIS) problem. Based on the basic property of the MIS, which forbids mutually adjoining vertices, the proposed algorithm derives the solution by repeatedly selecting vertices in the ascending order of their degree, given that the degree remains constant when vertices ${\nu}$ of the minimum degree ${\delta}(G)$ are selected and incidental edges deleted in a graph of n vertices. When applied to 22 graphs, the proposed algorithm could obtain the MIS visually yet effortlessly. The proposed linear MIS algorithm of time complexity O(n) always executes ${\alpha}(G)$ times, the cardinality of the MIS, and thus could be applied as a general algorithm to the MIS problem.

• The Korean Journal of Applied Statistics
• /
• v.27 no.4
• /
• pp.645-653
• /
• 2014

P-value is the probability of observing a current sample and possibly other samples departing equally or more extremely from the null hypothesis toward postulated alternative hypothesis. When p-value is less than a certain level called ${\alpha}$(= 0:05), researchers claim that the alternative hypothesis is supported empirically. Unfortunately, some findings discovered in that way are not reproducible, partly because the p-value itself is a statistic vulnerable to random variation. Boos and Stefanski (2011) suggests calculating the upper limit of p-value in hypothesis testing, using a bootstrap predictive distribution. To determine the sample size of a replication study, this study proposes thought experiments by simulating boosted bootstrap samples of different sizes from given observations. The method is illustrated for the cases of two-group comparison and multiple linear regression. This study also addresses the reproducibility of the points in the given 95% confidence interval. Numerical examples show that the center point is covered by 95% confidence intervals generated from bootstrap resamples. However, end points are covered with a 50% chance. Hence this study draws the graph of the reproducibility rate for each parameter in the confidence interval.