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The threshold for combs in random graphs
For let denote the tree consisting of an
-vertex path with disjoint -vertex paths beginning at each of its
vertices. An old conjecture says that for any the threshold for the
random graph to contain is at .
Here we verify this for with any fixed . In a companion
paper, using very different methods, we treat the complementary range, proving
the conjecture for (with ).Comment: 9 page
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