Arbitrary Orientations of Hamilton Cycles in Oriented Graphs
Copyright policy )Arbitrary Orientations of Hamilton Cycles in Oriented Graphs
We use a randomised embedding method to prove that for all $\alpha>0$ any sufficiently large oriented graph $G$ with minimum in-degree and out-degree $\delta^+(G),\delta^-(G)\geq (3/8+\alpha)|G|$ contains every possible orientation of a Hamilton cycle. This confirms a conjecture of Häggkvist and Thomason.
Eulerian and Hamiltonian graphs, Connectivity, oriented graph, randomized embedding method, Directed graphs (digraphs), tournaments, orientation, 05C38, 05C20; 05C38; 05C45; 05C35, Hamilton cycle, FOS: Mathematics, Mathematics - Combinatorics, 05C20, Combinatorics (math.CO), 05C35, Paths and cycles, 05C45
Eulerian and Hamiltonian graphs, Connectivity, oriented graph, randomized embedding method, Directed graphs (digraphs), tournaments, orientation, 05C38, 05C20; 05C38; 05C45; 05C35, Hamilton cycle, FOS: Mathematics, Mathematics - Combinatorics, 05C20, Combinatorics (math.CO), 05C35, Paths and cycles, 05C45
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