On the Depth of a Random Graph
On the Depth of a Random Graph
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In our eReader you can find the full English version of the book. Read On the Depth of a Random Graph Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book On the Depth of a Random Graph
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+ 2 k |B | we get |S k | > (2 k+1 - 1)|B |, implying • 10- k = log (Ji + 1) - 1 B o log {» "JILL + i) - i 2 6 log n ig ___ — - log Log n - 1 2 S k + 2B k > J (1 -c) + y (1 - c) So, we proved that: LEMMA 2. 2 : Conditioned on the event E, the BFS process will visit at least n(l - e) nodes of G f in_ T stages where x 1 - n~^ +1 .
Let us allow the BFS to continue until it can visit no more vertices, and let f be the final stage (such that |Bf + j| = 0). Consider the stage f n - log n or |B f / +...1 | = 0. After f" either the process stops or there are at most 6* log n nodes more to visit and this cannot take more than 6* log n stages in either case. At f, the set B^, , of "unvisited" nodes is at least of size 5* log n. Consider the backward process in which the set of unvisited nodes increases as stages are -1 1- \, cuted n revi se. Che nev iroces; Is syi imetrii to th BFS and because of the symmetry we can argue that: LEMMA 2.
What to read after On the Depth of a Random Graph?
You can find similar books in the "Read Also" column, or choose other free books by J H John H Reif to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
+ 2 k |B | we get |S k | > (2 k+1 - 1)|B |, implying • 10- k = log (Ji + 1) - 1 B o log {» "JILL + i) - i 2 6 log n ig ___ — - log Log n - 1 2 S k + 2B k > J (1 -c) + y (1 - c) So, we proved that: LEMMA 2. 2 : Conditioned on the event E, the BFS process will visit at least n(l - e) nodes of G f in_ T stages where x 1 - n~^ +1 .
Let us allow the BFS to continue until it can visit no more vertices, and let f be the final stage (such that |Bf + j| = 0). Consider the stage f n - log n or |B f / +...1 | = 0. After f" either the process stops or there are at most 6* log n nodes more to visit and this cannot take more than 6* log n stages in either case. At f, the set B^, , of "unvisited" nodes is at least of size 5* log n. Consider the backward process in which the set of unvisited nodes increases as stages are -1 1- \, cuted n revi se. Che nev iroces; Is syi imetrii to th BFS and because of the symmetry we can argue that: LEMMA 2.
What to read after On the Depth of a Random Graph?
You can find similar books in the "Read Also" column, or choose other free books by J H John H Reif to read onlineMoreLess
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