Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoi...

In this paper, we investigate the well-studied Hamiltonian cycle problem, and present an interesting dichotomy result on split graphs. T. Akiyama, T. Nishizeki, and N. Saito [22] have shown that the Hamiltonian cycle problem is NP-complete in planar bipartite graph with maximum degree 3. Using this reduction, we show that the Hamiltonian cycle problem is NP-complete in split graphs. In particul...

Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar. Preface Graph theory as a very popular area of discrete mathematics has rapidly been developed over the last couple of decades. Numerous theoretical results and countless applications to practical problems have been discovered. The concepts of k-ordered graphs and out-arc pancyclicity are two recent topics i...

A hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Theorems by Dirac and Ore, presenting sufficient conditions for a graph to be hamiltonian, are generalized to k-ordered hamiltonian graphs. The existence of k-ordered graphs with small m...

We prove a suucient condition for graphs to be hamiltonian. This result generalizes ve suucient conditions for hamiltonian graphs and is non-comparable with many well-known ones.

In [2], Brousek characterizes all triples of graphs, G1, G2, G3, with Gi = K1,3 for some i = 1, 2, or 3, such that all G1G2G3-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G1, G2, G3, none of which is a K1,s, s ≥ 3 such that G1, G2, G3-free graphs of sufficiently large order contain a hamiltonian cycle. In...