Expressions for the perfect matching numbers of cubicl x m x n lattices and their asymptotic values

1996 ◽  
Vol 20 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Hideyuki Narumi ◽  
Hideaki Kita ◽  
Haruo Hosoya
Keyword(s):  
Perfect Matching ◽  
Asymptotic Values

An expression for the perfect matching number of cubic 2 �m �n lattices and their asymptotic values

1994 ◽  
Vol 16 (1) ◽  
pp. 221-228 ◽  
Author(s):  
Hideyuki Narumi ◽  
Hideaki Kita ◽  
Haruo Hosoya
Keyword(s):  
Perfect Matching ◽  
Matching Number ◽  
Asymptotic Values

scholarly journals Random-Player Maker-Breaker games

10.37236/5032 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Michael Krivelevich ◽  
Gal Kronenberg
Keyword(s):  
Perfect Matching ◽  
Winning Strategy ◽  
Hamilton Cycle ◽  
The Other ◽  
Natural Question ◽  
Vertex Connectivity ◽  
Asymptotic Values ◽  
Player Game ◽  
Matching Game ◽  
As If

In a $(1:b)$ Maker-Breaker game, one of the central questions is to find the maximal value of $b$ that allows Maker to win the game (that is, the critical bias $b^*$). Erdős conjectured that the critical bias for many Maker-Breaker games played on the edge set of $K_n$ is the same as if both players claim edges randomly. Indeed, in many Maker-Breaker games, "Erdős Paradigm" turned out to be true. Therefore, the next natural question to ask is the (typical) value of the critical bias for Maker-Breaker games where only one player claims edges randomly. A random-player Maker-Breaker game is a two-player game, played the same as an ordinary (biased) Maker-Breaker game, except that one player plays according to his best strategy and claims one element in each round, while the other plays randomly and claims $b$ (or $m$) elements. In fact, for every (ordinary) Maker-Breaker game, there are two different random-player versions; the $(1:b)$ random-Breaker game and the $(m:1)$ random-Maker game. We analyze the random-player version of several classical Maker-Breaker games such as the Hamilton cycle game, the perfect-matching game and the $k$-vertex-connectivity game (played on the edge set of $K_n$). For each of these games we find or estimate the asymptotic values of the bias (either $b$ or $m$) that allow each player to typically win the game. In fact, we provide the "smart" player with an explicit winning strategy for the corresponding value of the bias.

scholarly journals Time Evolution of Initial Errors in Lorenz’s 05 Chaotic Model

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Hynek Bednář ◽  
Aleš Raidl ◽  
Jiří Mikšovský
Keyword(s):  
Weather Prediction ◽  
Prediction Method ◽  
Atmospheric Model ◽  
Ensemble Prediction ◽  
Asymptotic Value ◽  
Time Limits ◽  
Initial Errors ◽  
Asymptotic Values ◽  
Chaotic Model ◽  
Almost All

Initial errors in weather prediction grow in time and, as they become larger, their growth slows down and then stops at an asymptotic value. Time of reaching this saturation point represents the limit of predictability. This paper studies the asymptotic values and time limits in a chaotic atmospheric model for five initial errors, using ensemble prediction method (model’s data) as well as error approximation by quadratic and logarithmic hypothesis and their modifications. We show that modified hypotheses approximate the model’s time limits better, but not without serious disadvantages. We demonstrate how hypotheses can be further improved to achieve better match of time limits with the model. We also show that quadratic hypothesis approximates the model’s asymptotic value best and that, after improvement, it also approximates the model’s time limits better for almost all initial errors and time lengths.

scholarly journals Infinitely many equivalent versions of the graceful tree conjecture

2015 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Tao-Ming Wang ◽  
Cheng-Chang Yang ◽  
Lih-Hsing Hsu ◽  
Eddie Cheng
Keyword(s):  
Perfect Matching ◽  
Absolute Difference ◽  
Extra Condition ◽  
Graceful Labeling ◽  
The Absolute

A graceful labeling of a graph with q edges is a labeling of its vertices using the integers in [0, q], such that no two vertices are assigned the same label and each edge is uniquely identified by the absolute difference between the labels of its endpoints. The well known Graceful Tree Conjecture (GTC) states that all trees are graceful, and it remains open. It was proved in 1999 by Broersma and Hoede that there is an equivalent conjecture for GTC stating that all trees containing a perfect matching are strongly graceful (graceful with an extra condition). In this paper we extend the above result by showing that there exist infinitely many equivalent versions of the GTC. Moreover we verify these infinitely many equivalent conjectures of GTC for trees of diameter at most 7. Among others we are also able to identify new graceful trees and in particular generalize the ?-construction of Stanton-Zarnke (and later Koh- Rogers-Tan) for building graceful trees through two smaller given graceful trees.

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