Finding a hamiltonian cycle in the square of a block
Hang T. Lau · 1980
The subject of the thesis belongs to the theory of graphs. In 1966, C. St. J.A. Nash-Williams conjectured that the square of a block is hamiltonian. This conjecture quickly gained a wide popularity and, at the end of 1970, it was established by H. Fleischner. His proof of the existence of a hamiltonian cycle in the square of a block does not explicitly provide an algorithm for finding the cycle. The thesis will describe such an algorithm, with a running time O(n('2)) on every input with n vertices. For the most part, our algorithm follows closely the original lines of Fleischner's proof. The main difference occurs at the part where Fleischner proves the existence of a certain spanning subgraph in every connected bridgeless graph: we replace Fleischner's argument by a radically different one. This is the main original result of our thesis.