Structures of Domination in Graphs
暫譯: 圖中的支配結構

本卷包含17篇貢獻，介紹圖支配的進階主題，涵蓋未解決的問題、現代技術和最新成果。該書分為三個部分。第一部分專注於幾個與支配相關的概念：廣播支配、聯盟、支配數、支配著色、圖中的冗餘性、私有鄰居概念、遊戲支配、各種羅馬支配以及光譜圖論。第二部分涵蓋超圖、棋盤、導向圖和錦標賽中的支配問題。第三部分專注於簽名支配、負支配和多數支配、功率支配以及圖中的聯盟的演算法和複雜性發展。第三部分還包括一章關於自穩定演算法的內容。對讀者特別有益的是，第一章包含了常用術語的詞彙表。

本書旨在為在支配和圖論領域的成熟研究人員以及希望獲得所涵蓋主題知識的研究生提供參考，並概述該領域的主要成就和證明技術。

Teresa W. Haynes has focused her research on domination in graphs for over 30 years and is perhaps best known for coauthoring the 1998 book Fundamentals of Domination in Graphs and the companion volume Domination in Graphs: Advanced Topics. She has also co-edited 2 volumes in Springer's Problem Books in Mathematics Graph Theory: Favorite Conjectures and Open Problems. Haynes is also a co-author of the Springer Briefs in Mathematics From Domination to Coloring: The Graph Theory of Stephen T. Hedetniemi. Upon receiving her PhD from the University of Central Florida in 1988, she joined East Tennessee State University, where she is currently professor in the Department of Mathematics and Statistics. Haynes has coauthored more than 200 papers on domination and domination-related concepts, which introduced some of the most studied concepts in domination, such as power domination, paired domination, double domination, alliances and broadcasts in graphs, and stratified domination.

Stephen T. Hedetniemi is one of the earliest pioneers of domination in graphs along with E. J. Cockayne, who together proposed the theory of domination in graphs, in one of the most cited papers in the field in 1977. He received his PhD from the University of Michigan in 1966, with two world-class advisors, graph theorist Frank Harary, and the pioneer of genetic algorithms and MacArthur Fellowship winner, John Holland. He coauthored, the first book on domination in 1988 Fundamentals of Domination in Graphs, and co-edited a second book, Domination in Graphs: Advanced Topics. He also co-edited 2 volumes in Springer's Problem Books in Mathematics Graph Theory: Favorite Conjectures and Open Problems. Since 1974 he has coauthored more than 300 papers, 180 of which are on domination and domination-related concepts. Hedetniemi has introduced some of the most-studied concepts in domination theory, including total domination, independent domination, irredundance, Roman domination, power domination, alliances in graphs, signed and minus domination, fractional domination, domatic numbers, domination in grid graphs and chessboards, the first domination algorithms, the first domination NP-completeness results, and the first self-stabilizing domination algorithms. After leaving the University of Michigan, he taught computer science at the University of Iowa, and the University of Virginia, spent a visiting year at the University of Victoria with E. J. Cockayne, and then became department head of Computer and information Science at the University of Oregon. Since 1982 has been at Clemson University, where he served a five-year term as department head, and served on the Executive Committee of the Computing Accreditation Commission of ABET, Inc. He is currently Emeritus Professor of Computer Science in the School of Computing at Clemson University.

Michael A. Henning has devoted much of his research interests to the field of domination theory in graphs. He has been both plenary and invited speakers at several international conferences and is a prolific researcher having published over 460 papers to date in international mathematics journals. Henning was born and schooled in South Africa having obtained his PhD at the University of Natal in April 1989. In January 1989, he started his academic career as a lecturer at the University of Zululand, before accepting a lectureship in mathematics at the former University of Natal in January 1991. In January 2000, he was appointed a full professor at the University of Natal, which later merged with the University of Durban-Westville to form the University of KwaZulu-Natal in January 2004. After spending almost 20 years at the University of KwaZulu-Natal and one of its predecessors, the University of Natal, Michael moved to the University of Johannesburg in May 2010 as a research professor. He co-authored a Springer Briefs in Mathematics From Domination to Coloring: The Graph Theory of Stephen T. Hedetniemi and co-authored the Springer Monographs in Mathematics book Total Domination in Graphs and in 2020, he co-authored Springer's Developments in Mathematics book Transversals in Linear Uniform Hypergraphs.

特蕾莎·W·海恩斯專注於圖論中的支配研究已超過30年，並且因共同撰寫1998年的書籍圖論中的支配基礎及其伴隨卷圖論中的支配：進階主題而聞名。她還共同編輯了施普林格的數學問題書系列中的兩卷圖論：最受歡迎的猜想與未解問題。海恩斯也是施普林格數學簡報的共同作者，書名為從支配到著色：斯蒂芬·T·海德尼米的圖論。她於1988年在中佛羅里達大學獲得博士學位後，加入東田納西州立大學，目前擔任數學與統計系的教授。海恩斯共同撰寫了超過200篇有關支配及相關概念的論文，介紹了一些在支配理論中最受研究的概念，如功率支配、配對支配、雙重支配、圖中的聯盟與廣播，以及分層支配。

斯蒂芬·T·海德尼米是圖論中支配理論的早期先驅之一，與E·J·科克恩共同提出了支配理論，並於1977年發表了該領域最被引用的論文之一。他於1966年在密西根大學獲得博士學位，指導教授為圖論專家法蘭克·哈拉里和基因演算法的先驅、麥克阿瑟獎得主約翰·霍蘭德。他於1988年共同撰寫了第一本關於支配的書籍圖論中的支配基礎，並共同編輯了第二本書圖論中的支配：進階主題。他還共同編輯了施普林格的數學問題書系列中的兩卷圖論：最受歡迎的猜想與未解問題。自1974年以來，他共同撰寫了超過300篇論文，其中180篇專注於支配及相關概念。海德尼米引入了一些在支配理論中最受研究的概念，包括完全支配、獨立支配、冗餘性、羅馬支配、功率支配、圖中的聯盟、符號與負支配、分數支配、支配數、網格圖與棋盤上的支配、第一個支配演算法、第一個支配NP完全性結果，以及第一個自穩定支配演算法。在離開密西根大學後，他在愛荷華大學和維吉尼亞大學教授計算機科學，並在維多利亞大學與E·J·科克恩共度了一年，隨後成為俄勒岡大學計算機與資訊科學系的系主任。自1982年以來，他一直在克萊姆森大學任教，並擔任系主任五年，還曾在ABET, Inc.的計算機認證委員會執行委員會任職。目前他是克萊姆森大學計算學院的榮譽計算機科學教授。

邁克爾·A·亨寧將其研究興趣大部分投入於圖論中的支配理論。他曾在多個國際會議上擔任全體及特邀演講者，是一位多產的研究者，迄今已在國際數學期刊上發表超過460篇論文。亨寧出生並在南非接受教育，於1989年4月在納塔爾大學獲得博士學位。1989年1月，他開始在祖魯蘭大學擔任講師，然後於1991年1月接受納塔爾大學的數學講師職位。2000年1月，他被任命為納塔爾大學的正教授，該大學於2004年與德班-韋斯維爾大學合併，成立夸祖魯-納塔爾大學。在夸祖魯-納塔爾大學及其前身納塔爾大學工作近20年後，邁克爾於2010年5月轉至約翰尼斯堡大學擔任研究教授。他共同撰寫了施普林格數學簡報的從支配到著色：斯蒂芬·T·海德尼米的圖論，並共同撰寫了施普林格數學專著的書籍圖中的完全支配，在2020年，他共同撰寫了施普林格的數學發展書籍線性均勻超圖中的橫截面。