The Hamilton space of pseudorandom graphs
arxiv(2024)
摘要
We show that if n is odd and p ≥ C log n / n, then with high
probability Hamilton cycles in G(n,p) span its cycle space. More generally,
we show this holds for a class of graphs satisfying certain natural
pseudorandom properties. The proof is based on a novel idea of
parity-switchers, which can be thought of as analogues of absorbers in the
context of cycle spaces. As another application of our method, we show that
Hamilton cycles in a near-Dirac graph G, that is, a graph G with odd n
vertices and minimum degree n/2 + C for sufficiently large constant C, span
its cycle space.
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