A circulant digraph Circ(n;\, S) is a digraph with vertex set Zn and arcs from v to v+s for each v in Zn, and s in S. The bachelor thesis deals with existence of Hamilton cycle in circulant digraphs with outdegree 2 or 3. Hamilton cycle of a digraph is a closed walk, which meets every vertex exactly ones. Due to Rankin the hamiltonicity question of circulant digraphs of outdegree 2 is solved since 1946. Circulant digraphs of outdegree 3 have however turned out to be more challenging. There are some families, for which we can prove the existence of a Hamilton cycle and some families, for which we can prove nonexistence of such a cycle, but for most of circulant digraphs of outdegree 3 we know nothing jet. In the bachelor thesis we take a close look at Rankin's result for circulant digraphs of outdegree 2 and previous results that consider circulant digraphs of outdegree 3. Besides that we use computer program to examine the hamiltonicity of circulant digraphs of outdegree 3, that have 87 or less vertices.
|
