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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?