1996
DOI: 10.1006/jctb.1996.0036
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Sudden Emergence of a Giantk-Core in a Random Graph

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Cited by 424 publications
(506 citation statements)
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References 25 publications
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“…If J ≥ J then |A∩A | is bounded by (14), and if J ≤ J then |A∩A | is bounded by (15). Therefore, w.h.p.…”
Section: Proofmentioning
confidence: 95%
See 1 more Smart Citation
“…If J ≥ J then |A∩A | is bounded by (14), and if J ≤ J then |A∩A | is bounded by (15). Therefore, w.h.p.…”
Section: Proofmentioning
confidence: 95%
“…The proof of our theorem will be reminiscent of studies of the k-core, the pure literal rule, and other similar problems [14,11,6,7,9]. There, one repeatedly removes vertices (literals, etc.)…”
Section: Introductionmentioning
confidence: 99%
“…The sharpness of the threshold for the emergence of a non trivial k-core has already been proved in [7], where the threshold function is computed precisely for every k ≥ 3. It is shown that the threshold function is λ k n for a constant λ k > 0 which is computed in the paper.…”
Section: Letmentioning
confidence: 93%
“…The first determination of the threshold of existence of a k-core in a random graph was given by Pittel, Spencer and the second author [18].…”
Section: Preliminariesmentioning
confidence: 99%