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Pancyclic and Bipancyclic Graphs

  • Book
  • © 2016

Overview

Authors:
  1. John C. George

    1. BARNESVILLE, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Abdollah Khodkar

    1. Department of Mathematics, University of West Georgia, Carrollton, USA

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    You can also search for this author in PubMed   Google Scholar

  3. W.D. Wallis

    1. Department of Mathematics, Southern Illinois University, Evansville, USA

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    You can also search for this author in PubMed   Google Scholar

  • Provides an up-to-date survey on pancyclic and bipartite graphs
  • Surveys fundamental ideas of graph theory
  • Creates a clear overview of the field via unified terminology
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Graphs

    • John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 1-7

  3. Degrees and Hamiltoneity

    • John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 9-20

  4. Pancyclicity

    • John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 21-34

  5. Minimal Pancyclicity

    • John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 35-47

  6. Uniquely Pancyclic Graphs

    • John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 49-67

  7. Bipancyclic Graphs

    • John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 69-80

  8. Uniquely Bipancyclic Graphs

    • John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 81-97

  9. Minimal Bipancyclicity

    • John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 99-106

  10. Back Matter

    Pages 107-108
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Keywords

About this book

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 graphs contain cycles of all possible lengths from three up to the number of vertices in the graph. Bipartite graphs contain only cycles of even lengths, a bipancyclic graph is defined to be a bipartite graph with cycles of every even size from 4 vertices up to the number of vertices in the graph. Cutting edge research and fundamental results on pancyclic and bipartite graphs from a wide range of journal articles and conference proceedings are composed in this book to create a standalone presentation.

The following questions are highlighted through the book:

- What is the smallest possible number of edges in a pancyclic graph with v vertices?

- When do pancyclic graphs exist with exactly one cycle of every possible length?

- What is the smallest possible number of edges in a bipartite graph with v vertices?

- When do bipartite graphs exist with exactly one cycle of every possible length?

Reviews

“In this book, the authors give a simple survey about the sufficient conditions for a graph to be pancyclic (uniquely bipancyclic). Moreover, the authors give the proofs of some classic results which are useful tools to study and generalize cycle problems. Therefore, this book can help students and researchers alike to find inspiration and ideas on pancyclic and bipancyclic problems.” (Junqing Cai, Mathematical Reviews, February, 2017)

Authors and Affiliations

  • BARNESVILLE, USA

    John C. George

  • Department of Mathematics, University of West Georgia, Carrollton, USA

    Abdollah Khodkar

  • Department of Mathematics, Southern Illinois University, Evansville, USA

    W.D. Wallis

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