Random graphs, geometry and asymptotic structure
著者
書誌事項
Random graphs, geometry and asymptotic structure
(London Mathematical Society student texts, 84)
Cambridge University Press, 2016
- : hardback
- : pbk
大学図書館所蔵 全22件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and index
内容説明・目次
内容説明
The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.
目次
- Editors' introduction
- Part I. Long Paths and Hamiltonicity in Random Graphs: 1. Introduction
- 2. Tools
- 3. Long paths in random graphs
- 4. The appearance of Hamilton cycles in random graphs
- References for Part I
- Part II. Random Graphs from Restricted Classes: 1. Introduction
- 2. Random trees
- 3. Random graphs from block-stable classes
- References for Part II
- Part III. Lectures on Random Geometric Graphs: 1. Introduction
- 2. Edge counts
- 3. Edge counts: normal approximation
- 4. The maximum degree
- 5. A sufficient condition for connectivity
- 6. Connectivity and Hamiltonicity
- 7. Solutions to exercises
- References for Part III
- Part IV. On Random Graphs from a Minor-closed Class: 1. Introduction
- 2. Properties of graph classes
- 3. Bridge-addability, being connected and the fragment
- 4 Growth constants
- 5. Unlabelled graphs
- 6. Smoothness
- 7. Concluding remarks
- References for Part IV
- Index.
「Nielsen BookData」 より