Pancyclic and Bipancyclic Graphs
This book is focused on pancyclic and bipancyclic graphs and is geared toward researchers and graduate students in graph theory. Readers should be familiar with the basic concepts of graph theory, the definitions of a graph and of a cycle. Pancyclic graph
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John C. George Abdollah Khodkar W.D. Wallis
Pancyclic and Bipancyclic Graphs
123
SpringerBriefs in Mathematics
Series Editors Nicola Bellomo Michele Benzi Palle Jorgensen Tatsien Li Roderick Melnik Otmar Scherzer Benjamin Steinberg Lothar Reichel Yuri Tschinkel G. George Yin Ping Zhang
SpringerBriefs in Mathematics showcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied mathematicians. More information about this series at http://www.springer.com/series/10030
John C. George • Abdollah Khodkar • W.D. Wallis
Pancyclic and Bipancyclic Graphs
123
John C. George Department of Mathematics and Computer Science Gordon State College Barnesville, GA, USA
Abdollah Khodkar Department of Mathematics University of West Georgia Carrollton, GA, USA
W.D. Wallis Department of Mathematics Southern Illinois University Evansville, IN, USA
ISSN 2191-8198 ISSN 2191-8201 (electronic) SpringerBriefs in Mathematics ISBN 978-3-319-31950-6 ISBN 978-3-319-31951-3 (eBook) DOI 10.1007/978-3-319-31951-3 Library of Congress Control Number: 2016935702 © The Author(s) 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
The authors would like to dedicate this book to our families: Amanda and Robert (JCG); Sarah, Arvin, and Darian (AK); Ann (WDW)
Preface
For nearly 50 years, there has been some interest in the cycles occurring as subgraphs of graphs. In 1971, Adrian Bondy introduced the idea of a pancyclic graph, one that contained cycles of every possible length. But from that time, the idea has been largely unexplored. Together with some of our colleagues, we have
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