Graph theory experienced a tremendous growth in the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. This book aims to provide a solid background in the basic topics of graph theory. This is called the complete graph on ve vertices, denoted K5; in a complete graph, each vertex is connected to each of the others. Non-planar graphs can require more than four colors, for example this graph:. … Graph theory experienced a tremendous growth in the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. Intuitively, a problem isin P1 if thereisan efficient (practical) algorithm tofind a solutiontoit.On the other hand, a problem is in NP 2, if it is first efficient to guess a solution and then Acknowledgement These solutions are the result of taking CS-520(Advanced Graph Theory) course Graph theory experienced a tremendous growth in the 20th century. Ebook library B-OK.org | B–OK. It is shown that for each ϵ>0, there exist infinitely many n for each of which there exists a k-regular graph G of order n with k