A Density Result for Random Sparse Oriented Graphs and its Relation to a Conjecture of Woodall
نویسندگان
چکیده
We prove that for all ` ≥ 3 and β > 0 there exists a sparse oriented graph of arbitrarily large order with oriented girth ` and such that any 1/2+β proportion of its arcs induces an oriented cycle of length `. As a corollary we get that there exist infinitely many oriented graphs with vanishing density of oriented girth ` such that deleting any 1/`-fraction of their edges does not destroy all their oriented cycles. The proof is probabilistic.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 9 شماره
صفحات -
تاریخ انتشار 2002