Edge exchanges in hamiltonian decompositions of Kronecker-product graphs

On Edge Exchanges in Hamiltonian Decompositions of Kronecker-product Graphs

Let G be a connected graph on n vertices, and let ; ; and be edge-disjoint cycles in G such that (i) ; (resp. ;) are vertex-disjoint and (ii) jj + jj = jj+ jj = n, where jj denotes the length of. We say that ; ; and yield two edge-disjoint hamiltonian cycles by edge exchanges if the four cycles respectively contain edges e; f; g and h such that each of (? feg) S (? ffg) S fg; hg and (? fgg) S (...

Product of normal edge-transitive Cayley graphs

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

New Kronecker product decompositions and its applications

Firstly, two new kinds of Kronecker decompositions is developed, i.e. KPGD and KPID; Secondly, the sufficient and necessary conditions and algorithms of Kronecker product(KPD), KPGD, and KPID are discussed; At last, some useful properties of the rank of the sum of Kronecker product gemel decompositions are obtained.

Hamiltonian decompositions of random bipartite regular graphs

We prove a complete hamiltonian decomposition theorem for random bipartite regular graphs, thereby verifying a conjecture of Robinson and Wormald. The main step is to prove contiguity (a kind of asymptotic equivalence) of two probabilistic models of 4-regular bipartite graphs; namely, the uniform model, and the model obtained by taking the union of two independent, uniformly chosen bipartite Ha...

Hamiltonian decompositions of prisms over cubic graphs