explicit constructions using the local lemma

... permute the coins randomly, and then flip each of the coins The first and second coins come up heads, and the third comes up tails What is the probability that the first coin is the biased one? The ... the outcomes of the coin fl ips, each of the three coins is equally likely to be the biased one Let Ei be the event that the i th coin flipped is the biased one, and let B be the event that the ... repeatedly the following: choose one ball from the bin uniformly at random , and then put the bal l back i n the bin with another bal l of the same color We repeat u ntil there are n bal l s in the...

Ngày tải lên: 14/07/2016, 15:42

... the routers on the path is like a coupon collector’s problem If there’s n routers, then the expected number of packets arrived before destination host knows all of the routers on the path = nln(n) ...  The number of packets transmitted after the last sampled packet until and including the next sampled packet is geometrically distributed From the point of destination host, determining all the ... yj are compared with each other if they are not compared E[X] = ∑∑E[Xij] E[Xij] = 2/ (j-i+1) (when we choose either i or j from the set of Yij pivots {yi, yi+1, …, yj} Using k = j-i+1, we can compute...

Ngày tải lên: 12/07/2014, 18:20

... What does the distribution of the balls into the bins look like    “Birthday paradox” question: is there a bin with at least balls How many of the bins are empty? How many balls are in the fullest ... for m words in the dictionary New approach: chain hashing    Place the words into bins and search appropriate bin for the word The worlds in a bin: implemented as a linked list The placement ... possible password strings The collection of bins called hash table Chain hashing: items that fall into the same bin are chained together in a linked list Using a hash table turns the dictionary problem...

Ngày tải lên: 12/07/2014, 18:20

... edges, while in the other only extroverted edges [Problem Generalize these remarkable results to an arbitrary bidirected complete graph The all-negative case will be these theorems; the all-positive ... planarity using theta graphs J Graph Theory 27 (1998), 17–20 MR 98j:05055 Zbl 887.05016 A “claw” consists of a vertex and three incident half edges Let C be the set of claws in Γ and T the set of theta ... (1997a) for definitions of the Shi arrangements Here the characteristic polynomials of these and other arrangements are evaluated combinatorially §3: The Shi arrangements” §4: The Linial arrangement”:...

Ngày tải lên: 07/08/2014, 05:23

... log2 n , then we get from Theorem 5, that both r + ≤ k and r+1 + ≤ cannot be satisfied, and this completes the proof The proof of Theorem also proves Theorem Suppose, that there exists an explicitly ... , implying explicit Ramsey-graph constructions the electronic journal of combinatorics (2000), #R15 Theorem There exists a c > such that for all positive integer n, there exists an explicitly ... (better) constant than our c , using the famous Frankl-Wilson theorem [5] We also gave a construction, using the BBR polynomial [3] and also the Frankl-Wilson theorem in [6] A generalization...

Ngày tải lên: 07/08/2014, 06:20

... Using the same analysis of the expansion properties provides the same bound on p in Theorem 1.4 Triangle-free graphs: proof of Theorem 1.1 We will need the following lemma Let χ = χ(G) be the ... otherwise As usual the distance between two sets V1 and V2 of vertices in G is the length of the shortest path between u ∈ V1 and v ∈ V2 Lemma 2.1 Let G having the following properties: (a) The ... So if there are two short edges with distinct labels then there are at least two long edges in C in both directions along the cycle If the short edges of C all have the same label and they make...

Ngày tải lên: 07/08/2014, 06:20

... this path be v From the neighbors of the vertices on the path from v to i except for the vertices on the path, choose the neighbor w as the largest vertex less than j; Then add the new edge (w, ... an involution on the set Nn,k − Dn,k that reverses the parity of the number of free edges Theorem 3.3 There is an involution on the set Nn,k − Dn,k that reverses the parity of the number of free ... Let T1 be the first subtree of the root The map is defined by a recursive procedure • Step Assign a vertex as the root and let ψ(T1 ) be the first subtree of the root and its reflection be the third...

Ngày tải lên: 07/08/2014, 13:21

... K1,1,2 In either case, G contains an induced subgraph of order four or more that is uniquely hamiltonian The second part of the corollary is proved similarly, noting the following: (1) The only ... defines a graph to be a parity graph if, for every pair of vertices, the lengths of all the induced paths between them have the same parity This is equivalent to every cycle of odd length five ... B, with respect to the extension vertices x1 , , xn results from identifying the vertices xi and yi the electronic journal of combinatorics 15 (2008), #N36 for each i ≤ n (The vertex extension...

Ngày tải lên: 07/08/2014, 15:22

... when ∆ is regular with degree 57, we get the same contradiction The lemma is proved The next lemma will be used in the proof of Theorem 4.2 (see Section 4) Lemma 3.3 Let Γ be a strongly regular ... > If the µ-bound is attained, then µ = and Γ is the icosahedron, the Doro graph or the Conway–Smith graph Proof By Proposition 4.1, the graph Γ is a Terwilliger graph and, by Lemma 3.1, there ... Then α = and one of the following holds: (1) ∆ is the pentagon and Γ is the icosahedron; (2) ∆ is the Petersen graph and Γ is the Doro graph or the Conway–Smith graph; (3) ∆ is the Hoffman–Singleton...

Ngày tải lên: 08/08/2014, 12:22

... further extend their result to the last four bicyclic graphs These together with the previous result on the trees and unicyclic graphs, we can extend the ordering of connected graphs by their smallest ... from Lemma 2.1 and Theorem 1.1 The proof is completed the electronic journal of combinatorics 17 (2010), #R162 10 Acknowledgements The authors are indebted to the anonymous referees for their ... not isomorphic to B3 Then by Lemma 2.1 and Theorem 3.1, we have α(G) α(G′′ ) > α(B4 ) > α(G15 ) = α(G16 ) The proof is completed Now, we give the main result of this section Theorem 4.3 Let G ∈...

Ngày tải lên: 08/08/2014, 12:23

... that the structures of interest in these graphs are paths and cliques At the end of the section we prove the following theorem Theorem 3.1 Suppose A is a thin Lehman matrix Let W ⊂ V (GA ) be the ... Proof of Theorem 3.1 We may assume that W = [k] If W induces a path, then Lemma 3.2 proves the claim Otherwise, the connected component contains a triangle, so Lemma 3.14 implies k < r From the proof ... in the r cycle are not adjacent in GA Then A ≃ Cn Proof Let rows [k] correspond to the vertices of the cycle We must have k > in order r for the assumptions to hold Suppose A ≃ Cn Then by Lemma...

Ngày tải lên: 08/08/2014, 12:23

... women worked in the communications sector Twenty years later, though the number of men remained unchanged, the number of women rose to 550 000 A similar situation was seen in the wholesale and ... to 450 000 by 1995 The number of men grew only marginally from 425 000 to 480 000 over the same period In defence, the number of men declined from 225 000 to 200 000, while the number of women ... retail trade sector, where the number of women rose from about 550 000 in 1975 to almost 800 000 two decades later The number of men in this sector remained stable over the period, at around 700...

Ngày tải lên: 04/10/2012, 10:02

... number the total quantity the whole of the the majority the total the total number the whole amount the greatest amount the total amount all of the the full amount the greatest number the maximum the ... many of the following as is possible: The quantity of (the) workforce (the) banking sector fell The proportion of (the) workers increased The rate of The level of The percentage of (the) consumption ... (intransitive) or there is the idea that someone was responsible for the action E.g The number of unemployedpeople doubled in the lnst l0 years But: The out4tut of thefactory utas doubled uthen the neu...

Ngày tải lên: 04/10/2012, 10:02

... number the total quantity the whole of the the majority the total the total number the whole amount the greatest amount the total amount all of the the full amount the greatest number the maximum the ... many of the following as is possible: The quantity of (the) workforce (the) banking sector fell The proportion of (the) workers increased The rate of The level of The percentage of (the) consumption ... (intransitive) or there is the idea that someone was responsible for the action E.g The number of unemployedpeople doubled in the lnst l0 years But: The out4tut of thefactory utas doubled uthen the neu...

Ngày tải lên: 04/09/2013, 15:20

... if there are no issues, the paths of the affected node and all subordinates are updated based on the new manager’s path The logic used is to find the previous path of the updated node using the ... Output Regardless of the performance of the two queries listed in the previous section, the fact is that we haven’t really done much yet The output of either of these queries as they currently stand ... described in the section “Traversing the Graph,” but without the need to be concerned with cycles By ordering by the path, the output will follow the same nested order as the hierarchy itself The following...

Ngày tải lên: 05/10/2013, 08:48

... number the total quantity the whole of the the majority the total the total number the whole amount the greatest amount the total amount all of the the full amount the greatest number the maximum the ... from the graph, I c) the PoPulation ofAlia grew in the i" the 20th centur! I O1tltt groutth in the size of the As is shown/illustratedby the graph, | populationofAlia 20th century From the graph ... expressions in the table on the left with those on the right: The graph shows/ indicates I a) that thepopulationofAlia greu', It is clear from the table It can be seen from the graph I As the table...

Ngày tải lên: 25/10/2013, 07:20

... ofat the beginning; e.g The uater is then transported d) Vary the use of nouns and verbs: e.g instead of : The uater is then purifed write: Thepurifcation of uater is the next stageetc TASK 27 The ... consum?ilon;Production; emplqlment + all verbs except reduced the leuel of + the same as above for the rate of thepercentageof + the utorkforce ;the banking sector; (the) utorkers;consumption; declined; greu; production ... bacteria carriesthe nitrogen into the soil At tlte sametime somenitrogen-fixing bacteria in the nodulesof leguminousplants take the ninogen directlyfom the air The nitrogen in the soil is taken...

Ngày tải lên: 25/10/2013, 07:20

... lines connecting the points These lines will show increases and decreases The sharper the slope upward, the greater the increase The sharper the slope downward, the greater the decrease Line ... is given in the chart For example, the following chart shows the number of “Burger Sales for the Week of August 8−14.” The days of the week are given along the left side of the chart The number ... questions on the GRE may ask you to calculate percent increase or percent decrease The formula for figuring either of these is the same: amount of the change startingamount (follows the word from)...

Ngày tải lên: 01/11/2013, 14:20

... where the support graph is a rooted tree We characterize the reachable configurations and fixed points of the model At the end, we study the complexity as well as the local lattice structure of the ... relaxing the condition about the number of chips in a vertex, the evolution rule is much more flexible In other side, the obtained configuration space has not the lattice structure, and the convergence ... point Unfortunately, in the general CCFG, there are many fixed points in the configuration space and the structure of this space is quite complicate Nervertheless, in the case the support of a CCFG...

Ngày tải lên: 12/02/2014, 17:20