New Conditions for k-ordered Hamiltonian Graphs

We show that in any graph G on n vertices with d(x) + d(y) n for any two nonadjacent vertices x and y, we can fix the order of k vertices on a given cycle and find a hamiltonian cycle encountering these vertices in the same order, as long as k < n/12 and G is (k + 1)/2 -connected. Further we show that every 3k/2 connected graph on n vertices with d(x) + d(y) n for any two nonadjacent vertices x and y is k-ordered hamiltonian, i.e. for every ordered set of k vertices we can find a hamiltonian cycle encountering these vertices in the given order. Both connectivity bounds are best possible.

• Type: Journal
• Year: 2004
• Where: ARSCOM
• Authors: Guantao Chen, Ronald J. Gould, Florian Pfender
• Keywords: ARSCOM 2004, Connectivity Bounds, Hamiltonian Cycle, Nonadjacent Vertices