(k+1)-Cores Have k-Factors
نویسندگان
چکیده
We prove that almost surely the first non-empty (k+1)-core to arise during the random graph process will have a k-factor or will be k-factor-critical. Thus the threshold for the appearance of a k-regular subgraph is at most the threshold for the (k+1)-core. This improves a result of Pralat, Verstraete and Wormald [5] and proves a conjecture of Bollobas, Kim and Verstraete [3].
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 21 شماره
صفحات -
تاریخ انتشار 2012