Probability HAMILTON CYCLES IN RANDOM GEOMETRIC GRAPHS
نویسندگان
چکیده
We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penrose. We also show that in the k-nearest neighbour model, there is a constant κ such that almost every κ-connected graph has a Hamilton cycle.
منابع مشابه
A Brief Introduction to Hamilton Cycles in Random Graphs
We survey results concerning Hamilton cycles in random graphs. Specifically, we focus on existence results for general and regular graphs, and discuss algorithms for finding Hamilton cycles and solving related problems (that succeed with high probability).
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