本文選題：圖論 + 彼得森　； 參考：《河北師范大學(xué)》2015年碩士論文

【摘要】：圖論自1736年誕生之日起,在200多年的發(fā)展進(jìn)程中,數(shù)學(xué)家們圍繞著名的“四色問題”展開研究。20世紀(jì)以來,隨著圖論與其他學(xué)科的相互融合,涌現(xiàn)了諸如代數(shù)圖論、概率圖論、隨機(jī)圖論等眾多新的學(xué)科交叉分支。圖因子理論就是代數(shù)圖論的范疇,主要研究一般圖具有圖因子的圖特征問題。丹麥數(shù)學(xué)家彼得森的獨(dú)創(chuàng)性思維和學(xué)科交叉思想致使他創(chuàng)作出第一篇包含圖論方面(圖因子理論)基本結(jié)論的文章《正則圖理論》,其在圖因子理論的工作被認(rèn)為是具有開創(chuàng)性的。本文在整理、研讀、分析文獻(xiàn)的基礎(chǔ)上,結(jié)合圖因子理論發(fā)展歷史,以彼得森三篇圖論文章為核心展開具體研究,系統(tǒng)分析了彼得森解決問題的創(chuàng)新思維和學(xué)科交叉思想。全文主要討論了以下問題:1.詳細(xì)介紹了彼得森的生平。彼得森是19世紀(jì)下半葉丹麥數(shù)學(xué)的領(lǐng)軍人物之一,雖生活艱苦,但不忘數(shù)學(xué)研究。獨(dú)特的創(chuàng)造性和優(yōu)雅的教學(xué)態(tài)度,使其一生受到尊重,享有國際榮譽(yù)。2.概述了圖因子理論形成的學(xué)術(shù)背景。(1)泰特對“四色問題”的研究使得1-因子凸顯出來。(2)西爾維斯特將形象直觀的“圖”應(yīng)用于不變量理論的研究中,其方法為彼得森提供了創(chuàng)造性思維的來源。3.深究了彼得森在圖因子理論的工作。以彼得森的三篇圖論文章為核心展開細(xì)致研究,分析了《正則圖理論》的創(chuàng)作初衷、研究框架及主要結(jié)論。重點(diǎn)剖析了彼得森的兩個定理,簡要分析了作為泰特“定理”反例給出的彼得森圖以及彼得森在3-正則圖的工作。4.闡述了彼得森對圖因子理論后續(xù)發(fā)展的影響�；厮莶⒎治隽耸鼙说蒙ぷ饔绊懙目履嵯！㈤T格爾、霍爾、塔特在圖因子理論的重要工作,揭示彼得森的工作在圖因子理論后續(xù)發(fā)展的重要影響,進(jìn)而更加明確了彼得森工作的開創(chuàng)性地位。
[Abstract]:Since the birth of graph theory in 1736, in the course of more than 200 years' development, mathematicians have studied the famous "four-color problem" since the 20th century. With the integration of graph theory and other disciplines, such as algebraic graph theory and probabilistic graph theory have emerged. Random graph theory and many other new interdisciplinary branches. The theory of graph factor is the category of algebraic graph theory. The Danish mathematician Peterson's original thinking and interdisciplinary thinking led him to write the first article "regular Graph Theory", which contains the basic conclusions of graph theory (graph factor theory), and its work in graph factor theory is considered to be Is groundbreaking. On the basis of sorting out, studying and analyzing the literature, combined with the history of the development of graph factor theory and taking Peterson's three graph theory articles as the core, this paper systematically analyzes Peterson's innovative thinking and interdisciplinary thinking on problem-solving. This paper mainly discusses the following question: 1. The life of Peterson was introduced in detail. Peterson was one of the leaders of Danish mathematics in the second half of the 19 th century. Unique creative and elegant teaching attitude, so that its life is respected, enjoy international honor. 2. This paper summarizes the academic background of the formation of graph factor theory. (1) Tate's study of "four-color problem" makes 1- factor prominent. (2) Sylvester applies image "graph" to the study of invariant theory. The method provides Peterson with a source of creative thinking. In this paper, Peterson's work on graph factor theory is studied. Taking Peterson's three graph theory articles as the core, the author analyzes the original intention, the research frame and the main conclusions of the regular Graph Theory. In this paper, two Peterson's theorems are analyzed, and the Peterson graphs given as a counter example of Tate's Theorem and the work of Peterson's 3-regular graph. The influence of Peterson on the following development of graph factor theory is expounded. This paper reviews and analyzes the important work of Koenig, Mengar, Hall and Tate in graph factor theory, which is influenced by Peterson's work, and reveals the important influence of Peterson's work on the subsequent development of graph factor theory. Thus, the groundbreaking position of Peterson's work was more clearly defined.
【學(xué)位授予單位】：河北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O157.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前5條

1 程釗;;圖論中若干重要定理的歷史注記[J];數(shù)學(xué)的實(shí)踐與認(rèn)識;2013年01期

2 W.T.Tutte;劉彥佩;;我所了解的圖論(一)[J];運(yùn)籌學(xué)雜志;1984年01期

3 W.T.Tutte;劉彥佩;;我所了解的圖論(三)[J];運(yùn)籌學(xué)雜志;1985年01期

4 W.T.Tutte;劉彥佩;;我所了解的圖論(四)[J];運(yùn)籌學(xué)雜志;1985年02期

5 趙瑤瑤;汪曉勤;;鄒騰:19世紀(jì)數(shù)學(xué)史家、丹麥數(shù)學(xué)的先驅(qū)者[J];自然辯證法通訊;2007年03期

相關(guān)博士學(xué)位論文 前1條

1 王獻(xiàn)芬;塔特對圖論的貢獻(xiàn)[D];河北師范大學(xué);2010年

相關(guān)碩士學(xué)位論文 前1條

1 王麗麗;圖論的歷史發(fā)展研究[D];山東大學(xué);2012年

，

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